# Boundary Problem (boundary + problem)

Distribution by Scientific Domains

Kinds of Boundary Problem

 free boundary problem moving boundary problem

## Selected Abstracts

### Boundary Perturbation Methods for Water Waves

GAMM - MITTEILUNGEN, Issue 1 2007
David P. Nicholls
Abstract The most successful equations for the modeling of ocean wave phenomena are the free,surface Euler equations. Their solutions accurately approximate a wide range of physical problems from open,ocean transport of pollutants, to the forces exerted upon oil platforms by rogue waves, to shoaling and breaking of waves in nearshore regions. These equations provide numerous challenges for theoreticians and practitioners alike as they couple the difficulties of a free boundary problem with the subtle balancing of nonlinearity and dispersion in the absence of dissipation. In this paper we give an overview of, what we term, "Boundary Perturbation" methods for the analysis and numerical simulation of this "water wave problem". Due to our own research interests this review is focused upon the numerical simulation of traveling water waves, however, the extensive literature on the initial value problem and additional theoretical developments are also briefly discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

### Urban Textural Analysis from Remote Sensor Data: Lacunarity Measurements Based on the Differential Box Counting Method

GEOGRAPHICAL ANALYSIS, Issue 4 2006
Soe W. Myint
Lacunarity is related to the spatial distribution of gap or hole sizes. For low lacunarity, all gap sizes are the same and geometric objects are deemed homogeneous; conversely, for high lacunarity, gap sizes are variable and objects are therefore heterogeneous. Textures that are homogeneous at small scales can be quite heterogeneous at large scales and vice versa, and hence, lacunarity can be considered a scale-dependent measure of heterogeneity or texture. In this article, we use a lacunarity method based on a differential box counting approach to identify urban land-use and land-cover classes from satellite sensor data. Our methodology focuses on two different gliding box methods to compute lacunarity values and demonstrate a mirror extension approach for a local moving window. The extension approach overcomes, or at least minimizes, the boundary problem. The results from our study suggest that the overlapping box approach is more effective than the skipping box approach, but that there is no significant difference between window sizes. Our work represents a contribution to not only advances in textural and spatial metrics as used in remote-sensing pattern interpretation but also for broadening understanding of the computational geometry of nonlinear shape models of which lacunarity is the reciprocal of fractal theory. [source]

### Heat transfer characteristics in a two-dimensional channel with an oscillating wall

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2001
Masahide Nakamura
Abstract Numerical calculations have been carried out for the laminar heat transfer in a two-dimensional channel bounded by a fixed wall and an oscillating wall. In this calculation, the moving boundary problem was transformed into a fixed boundary problem using the coordinate transformation method, and the fully implicit finite difference method was used to solve the mass, momentum, and energy conservation equations. The calculated results are summarized as follows: (i) The wall oscillation has an effect of enhancing the heat transfer and an effect of increasing the additional pressure loss. (ii) An optimum Strouhal number for the enhancement of heat transfer exists, and this optimum value is strongly affected by the amplitude of wall oscillation. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 280,292, 2001 [source]

### Comparative study between two numerical methods for oxygen diffusion problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2009
Vildan GülkaçArticle first published online: 28 APR 200
Abstract Two approximate numerical solutions of the oxygen diffusion problem are defined using three time-level of Crank,Nicolson equation and Gauss,Seidel iteration for three time-level of implicit method. Oxygen diffusion in a sike cell with simultaneous absorption is an important problem and has a wide range of medical applications. The problem is mathematically formulated through two different stages. At the first stage, the stable case having no oxygen transition in the isolated cell is searched, whereas at the second stage the moving boundary problem of oxygen absorbed by the tissues in the cell is searched. The results obtained by three time-level of implicit method and Gauss,Seidel iteration for three time-level of implicit method and the results gave a good agreement with the previous methods (J. Inst. Appl. Math. 1972; 10:19,33; 1974; 13:385,398; 1978; 22:467,477). Copyright © 2008 John Wiley & Sons, Ltd. [source]

### Numerical simulation of the forest impact on aquifers

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2004
A. Leontiev
Abstract Here we propose a numerical method for the computer simulation of forest impact on aquifers. With this phenomenon we understand changes in the level of groundwater table beneath the areas recovered by trees. The mathematical model of the forest impact includes a boundary value problem with free and contact boundary conditions. Considering this free-contact boundary problem as a shape optimization problem we perform boundary elements discretization. Assuming the state and free boundary variables as independents, we treat the discretized problem as a non-linear mathematical program and apply interior point algorithm to solve it. Numerical results for an illustrative 2D test problem are discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2005
A. P. Peirce
Abstract We present a novel multigrid (MG) procedure for the efficient solution of the large non-symmetric system of algebraic equations used to model the evolution of a hydraulically driven fracture in a multi-layered elastic medium. The governing equations involve a highly non-linear coupled system of integro-partial differential equations along with the fracture front free boundary problem. The conditioning of the algebraic equations typically degrades as O(N3). A number of characteristics of this problem present significant new challenges for designing an effective MG strategy. Large changes in the coefficients of the PDE are dealt with by taking the appropriate harmonic averages of the discrete coefficients. Coarse level Green's functions for multiple elastic layers are constructed using a single dual mesh and superposition. Coarse grids that are sub-sets of the finest grid are used to treat mixed variable problems associated with ,pinch points.' Localized approximations to the Jacobian at each MG level are used to devise efficient Gauss,Seidel smoothers and preferential line iterations are used to eliminate grid anisotropy caused by large aspect ratio elements. The performance of the MG preconditioner is demonstrated in a number of numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Existence of front solutions for a nonlocal transport problem describing gas ionization

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2010
M. Günther
Abstract We discuss a moving boundary problem arising from a model of gas ionization in the case of negligible electron diffusion and suitable initial data. It describes the time evolution of an ionization front. Mathematically, it can be considered as a system of transport equations with different characteristics for positive and negative charge densities. We show that only advancing fronts are possible and prove short-time well posedness of the problem in Hölder spaces of functions. Technically, the proof is based on a fixed-point argument for a Volterra-type system of integral equations involving potential operators. It crucially relies on estimates of such operators with respect to variable domains in weighted Hölder spaces and related calculus estimates. Copyright © 2010 John Wiley & Sons, Ltd. [source]

### Interaction of elementary waves for scalar conservation laws on a bounded domain

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2003
Hongxia Liu
Abstract This paper is concerned with the interaction of elementary waves on a bounded domain for scalar conservation laws. The structure and large time asymptotic behaviours of weak entropy solution in the sense of Bardos et al. (Comm. Partial Differential Equations 1979; 4: 1017) are clarified to the initial,boundary problem for scalar conservation laws ut+,(u)x=0 on (0,1) × (0,,), with the initial data u(x,0)=u0(x):=um and the boundary data u(0,t)=u -,u(1,t)=u+, where u±,um are constants, which are not equivalent, and ,,C2 satisfies ,,,>0, ,(0)=f,(0)=0. We also give some global estimates on derivatives of the weak entropy solution. These estimates play important roles in studying the rate of convergence for various approximation methods to scalar conservation laws. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Single-phase flow in composite poroelastic media

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2002
R. E. Showalter
The mathematical formulation and analysis of the Barenblatt,Biot model of elastic deformation and laminar flow in a heterogeneous porous medium is discussed. This describes consolidation processes in a fluid-saturated double-diffusion model of fractured rock. The model includes various degenerate cases, such as incompressible constituents or totally fissured components, and it is extended to include boundary conditions arising from partially exposed pores. The quasi-static initial,boundary problem is shown to have a unique weak solution, and this solution is strong when the data are smoother. Copyright © 2002 John Wiley & Sons, Ltd. [source]

### Evolution free boundary problem for equations of viscous compressible heat-conducting capillary fluids

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2001
In the paper the global motion of a viscous compressible heat conducting capillary fluid in a domain bounded by a free surface is considered. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global-in-time solution which is close to the constant state for any moment of time. The solution is obtained in such Sobolev,Slobodetskii spaces that the velocity, the temperature and the density of the fluid have $W_2^{2+\alpha,1+\alpha/2}$\nopagenumbers\end, $W_2^{2+\alpha,1+\alpha/2}$\nopagenumbers\end and $W_2^{1+\alpha,1/2+\alpha/2}$\nopagenumbers\end ,regularity with ,,(¾, 1), respectively. Copyright © 2001 John Wiley & Sons, Ltd. [source]

### Asymptotic behaviour for a non-monotone fluid in one dimension: the positive temperature case

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2001
B. Ducomet
We consider a one-dimensional continuous model of neutron star, described by a compressible Navier,Stokes system with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We study the asymptotic behaviour of globally defined solutions of a mixed free boundary problem for our model, for large time, assuming that a sufficient thermal dissipation is present. Copyright © 2001 John Wiley & Sons, Ltd. [source]

### Eigenvalue asymptotics for a boundary problem involving an elliptic system

MATHEMATISCHE NACHRICHTEN, Issue 11 2006
M. Faierman
Abstract In a recent paper, Agranovich, Denk, and Faierman developed a method for deriving results pertaining to the eigenvalue asymptotics for scalar elliptic boundary problems involving a weight function under limited smoothness assumptions and under an ellipicity with parameter condition. Denk, Faierman, and Möller then used this method to extend the aforementioned results for the scalar case to the case of a homogeneous elliptic systems. However, the method of Agranovich et al. does not carry over to more general elliptic systems of Agmon,Douglis,Nirenberg type. By employing a different method, we are able to overcome this difficulty, and hence in this paper we derive results pertaining to the eigenvalue asymptotics for more general systems of Agmon,Douglis,Nirenberg type and under limited smoothness assumptions. Furthermore, our results not only subsume those of Denk et al., but are derived under much weaker smoothness assumptions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

### Rent Assistance Policy for Residents of Retirement Villages

AUSTRALASIAN JOURNAL ON AGEING, Issue 3 2000
Tony Eardley
Objectives: To assess whether policies on rent assistance for retirement village residents are targeting help towards those who need it, and to provide an information base for future policy decisions on eligibility for assistance. Method: A telephone survey of managers of a national sample of 52 retirement villages and a postal survey of residents in 49 of these villages. Results: The findings did not support the policy rationale that higher entry contributions were correlated with lower ongoing charges. Just over 40 per cent of residents of self-care housing and two-thirds of those in serviced apartments had paid entry contributions low enough for eligibility for rent assistance with their ongoing housing charges. Many of these were not, however, receiving assistance, mainly because their charges were below the minimum rent threshold. The distribution of reported levels of non-housing assets tended overall to match the varying levels of entry contributions, but half of those paying relatively high entry contributions still had low levels of both assets and income. Conclusions: It appears that targeting remains reasonably accurate for the majority of residents, but there is a potential boundary problem created by the eligibility and minimum rent thresholds. Thus a minority of residents may be disadvantaged compared with others in similar financial circumstances. [source]

### Existence and uniqueness of weak solutions for precipitation fronts: A novel hyperbolic free boundary problem in several space variables

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2010
Andrew J. Majda
The determination of the large-scale boundaries between moist and dry regions is an important problem in contemporary meteorology. These phenomena have been addressed recently in a simplified tropical climate model through a novel hyperbolic free boundary formulation yielding three families (drying, slow moistening, and fast moistening) of precipitation fronts. The last two wave types violate Lax's shock inequalities yet are robustly realized. This formal hyperbolic free boundary problem is given here a rigorous mathematical basis by establishing the existence and uniqueness of suitable weak solutions arising in the zero relaxation limit. A new L2 -contraction estimate is also established at positive relaxation values. © 2010 Wiley Periodicals, Inc. [source]

### Local existence for the free boundary problem for nonrelativistic and Relativistic compressible Euler equations with a vacuum boundary condition

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2009
Yuri Trakhinin
We study the free boundary problem for the equations of compressible Euler equations with a vacuum boundary condition. Our main goal is to recover in Eulerian coordinates the earlier well-posedness result obtained by Lindblad [11] for the isentropic Euler equations and extend it to the case of full gas dynamics. For technical simplicity we consider the case of an unbounded domain whose boundary has the form of a graph and make short comments about the case of a bounded domain. We prove the local-in-time existence in Sobolev spaces by the technique applied earlier to weakly stable shock waves and characteristic discontinuities [5, 12]. It contains, in particular, the reduction to a fixed domain, using the "good unknown" of Alinhac [1], and a suitable Nash-Moser-type iteration scheme. A certain modification of such an approach is caused by the fact that the symbol associated to the free surface is not elliptic. This approach is still directly applicable to the relativistic version of our problem in the setting of special relativity, and we briefly discuss its extension to general relativity. © 2009 Wiley Periodicals, Inc. [source]

### Geometry and a priori estimates for free boundary problems of the Euler's equation

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2008
Jalal Shatah
In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to 0, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension. © 2007 Wiley Periodicals, Inc. [source]

### A free boundary problem with optimal transportation

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 1 2004
Ovidiu Savin
First page of article [source]

### Boundary and border considerations in hydrology

HYDROLOGICAL PROCESSES, Issue 7 2004
Ming-ko Woo
Abstract This paper examines several issues related to hydrological boundaries and their border zones. In a two-dimensional space, a boundary is a line that separates two domains possessing different hydrological properties or dominated by different hydrological processes, and a border is an area that experiences an edge effect owing to transitions or mixing of processes. Hydrological boundaries may be static, such as drainage divides, or dynamic, such as the edges of a seasonal snow cover. They may be open or closed to the transfer of matter and energy, although most boundaries tend to be perforated, permitting different rates of movement across different segments. Borders may be narrow or the edge effect can affect large areas, as happens to the sensible heat flux over a highly fragmented melting snowfield. The introduction of artificial boundaries, notably the grid patterns of remote sensing pixels, digital elevation models and land surface schemes, gives rise to problems of mismatch with the natural hydrological boundaries. Incorrect demarcation, omission and generalization of boundaries can produce errors that are hard to rectify. Serious biases are involved when point observations are used to calibrate parameters or to validate model outputs integrated over a bounded area. Examples are drawn mainly from cold climate hydrology to illustrate the boundary issues but the questions transcend disciplinary areas. The intent of this presentation is to stimulate discussions that could be a prelude to finding solutions to many boundary problems which have thus far eluded hydrological investigations. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### Large eddy simulation of turbulent flows in complex and moving rigid geometries using the immersed boundary method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2005
Mayank Tyagi
Abstract A large eddy simulation (LES) methodology for turbulent flows in complex rigid geometries is developed using the immersed boundary method (IBM). In the IBM body force terms are added to the momentum equations to represent a complex rigid geometry on a fixed Cartesian mesh. IBM combines the efficiency inherent in using a fixed Cartesian grid and the ease of tracking the immersed boundary at a set of moving Lagrangian points. Specific implementation strategies for the IBM are described in this paper. A two-sided forcing scheme is presented and shown to work well for moving rigid boundary problems. Turbulence and flow unsteadiness are addressed by LES using higher order numerical schemes with an accurate and robust subgrid scale (SGS) stress model. The combined LES,IBM methodology is computationally cost-effective for turbulent flows in moving geometries with prescribed surface trajectories. Several example problems are solved to illustrate the capability of the IBM and LES methodologies. The IBM is validated for the laminar flow past a heated cylinder in a channel and the combined LES,IBM methodology is validated for turbulent film-cooling flows involving heat transfer. In both cases predictions are in good agreement with measurements. LES,IBM is then used to study turbulent fluid mixing inside the complex geometry of a trapped vortex combustor. Finally, to demonstrate the full potential of LES,IBM, a complex moving geometry problem of stator,rotor interaction is solved. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### M -functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems

MATHEMATISCHE NACHRICHTEN, Issue 3 2009
B. M. Brown
Abstract In this paper, we combine results on extensions of operators with recent results on the relation between the M -function and the spectrum, to examine the spectral behaviour of boundary value problems. M -functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the operator to possess spectral points that cannot be detected by the M -function (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

### Eigenvalue asymptotics for a boundary problem involving an elliptic system

MATHEMATISCHE NACHRICHTEN, Issue 11 2006
M. Faierman
Abstract In a recent paper, Agranovich, Denk, and Faierman developed a method for deriving results pertaining to the eigenvalue asymptotics for scalar elliptic boundary problems involving a weight function under limited smoothness assumptions and under an ellipicity with parameter condition. Denk, Faierman, and Möller then used this method to extend the aforementioned results for the scalar case to the case of a homogeneous elliptic systems. However, the method of Agranovich et al. does not carry over to more general elliptic systems of Agmon,Douglis,Nirenberg type. By employing a different method, we are able to overcome this difficulty, and hence in this paper we derive results pertaining to the eigenvalue asymptotics for more general systems of Agmon,Douglis,Nirenberg type and under limited smoothness assumptions. Furthermore, our results not only subsume those of Denk et al., but are derived under much weaker smoothness assumptions. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

### Radial basis function Hermite collocation approach for the numerical simulation of the effect of precipitation inhibitor on the crystallization process of an over-saturated solution

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2006
A. Hernandez Rosales
Abstract This work is concerned with the analysis of the effect of precipitation inhibitors on the growth of crystals from over-saturated solutions, by the numerical simulation of the fundamental mechanisms of such crystallization process. The complete crystallization process in the presence of precipitation inhibitor is defined by a set of coupled partial differential equations that needs to be solved in a recursive manner, due to the inhibitor modification of the molar flux of the mineral at the crystal interface. This set of governing equations needs to satisfy the corresponding initial and boundary conditions of the problem where it is necessary to consider the additional unknown of a moving interface, i.e., the growing crystal surface. For the numerical solution of the proposed problem, we used a truly meshless numerical scheme based upon Hermite interpolation property of the radial basis functions. The use of a Hermitian meshless collocation numerical approach was selected in this work due to its flexibility on dealing with moving boundary problems and their high accuracy on predicting surface fluxes, which is a crucial part of the diffusion controlled crystallization process considered here. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source]

### Coupling finite difference methods and integral formulas for elliptic problems arising in fluid mechanics

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2004
C. Albuquerque
Abstract This article is devoted to the numerical analysis of two classes of iterative methods that combine integral formulas with finite-difference Poisson solvers for the solution of elliptic problems. The first method is in the spirit of the Schwarz domain decomposition method for exterior domains. The second one is motivated by potential calculations in free boundary problems and can be viewed as a numerical analytic continuation algorithm. Numerical tests are presented that confirm the convergence properties predicted by numerical analysis. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 199,229, 2004 [source]

### On Comparison of Mixture Models for Closed Population Capture,Recapture Studies

BIOMETRICS, Issue 2 2009
Chang Xuan Mao
Summary A mixture model is a natural choice to deal with individual heterogeneity in capture,recapture studies. Pledger (2000, Biometrics56, 434,442; 2005, Biometrics61, 868,876) advertised the use of the two-point mixture model. Dorazio and Royle (2003, Biometrics59, 351,364; 2005, Biometrics61, 874,876) suggested that the beta-binomial model has advantages. The controversy is related to the nonidentifiability of the population size (Link, 2003, Biometrics59, 1123,1130) and certain boundary problems. The total bias is decomposed into an intrinsic bias, an approximation bias, and an estimation bias. We propose to assess the approximation bias, the estimation bias, and the variance, with the intrinsic bias excluded when comparing different estimators. The boundary problems in both models and their impacts are investigated. Real epidemiological and ecological examples are analyzed. [source]

### Picking up the pieces: local government reorganisation and voluntary sector children's services

CHILDREN & SOCIETY, Issue 2 2000
Gary Craig
Between 1995 and 1998, most of British local government was reorganised, leading to the creation of more, generally smaller, local authorities. Although social services were then the direct responsibility of local government, the potential impact of reorganisation on social work departments and partner organisations was barely considered prior to reorganisation. This article explores the consequences of reorganisation for children's services provided by voluntary sector organisations in Scotland, England and Wales. Drawing on two separate but complementary studies, the paper reviews the impact on funding, boundary problems, changing structures and the fragmentation of local authorities. It concludes that although some advances may be stimulated in the medium term by reorganisation, the overall short-term impact for projects and their users is likely to have been damaging. Copyright © 2000 John Wiley & Sons, Ltd. [source]

### Geometry and a priori estimates for free boundary problems of the Euler's equation

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2008
Jalal Shatah
In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to 0, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler flow with zero surface tension. © 2007 Wiley Periodicals, Inc. [source]