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Stationary Problem (stationary + problem)
Selected AbstractsThe steady states and convergence to equilibria for a 1-D chemotaxis model with volume-filling effectMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2010Yanyan Zhang Abstract We consider a chemotaxis model with volume-filling effect introduced by Hillen and Painter. They also proved the existence of global solutions for a compact Riemannian manifold without boundary. Moreover, the existence of a global attractor in W1, p(,,,n), p>n, p,2, was proved by Wrzosek. He also proved that the ,-limit set consists of regular stationary solutions. In this paper, we prove that the 1-D stationary problem has at most an infinitely countable number of regular solutions. Furthermore, we show that as t,, the solution of the 1-D evolution problem converges to an equilibrium in W1, p, p,2. Copyright © 2009 John Wiley & Sons, Ltd. [source] Stationary solutions to the drift,diffusion model in the whole spacesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2009Ryo Kobayashi Abstract We study the stationary problem in the whole space ,n for the drift,diffusion model arising in semiconductor device simulation and plasma physics. We prove the existence and uniqueness of stationary solutions in the weighted Lp spaces. The proof is based on a fixed point theorem of the Leray,Schauder type. Copyright © 2008 John Wiley & Sons, Ltd. [source] Asymptotic behaviour of solutions of quasilinear evolutionary partial differential equations of parabolic type on unbounded spatial intervalsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2006Poul Abstract We study the long-time behaviour of solutions to a quasilinear parabolic problem on a half-line. The main result lies in showing the existence of a positive solution that converges to the travelling wave of solution to the stationary problem on the whole line. The main tools used here are the zero number theory and the concentration compactness principle. This result is a generalization of a result know for semilinear parabolic equations. Copyright © 2006 John Wiley & Sons, Ltd. [source] An asymptotic-induced one-dimensional model to describe fires in tunnels II: the stationary problemMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2003Ingenuin Gasser Abstract We study stationary solutions of a one-dimensional low-Mach-number model derived in Gasser and Struckmeier (Math. Meth. Appl. Sci. 2002; 25(14): 1231) to describe fire events in long tunnels. The existence of solutions of the corresponding stationary model is shown to be equivalent to the existence of solutions of an algebraic problem. Multiple solutions are shown to be possible. The relation between different formulations of the problem is analysed. Weak and special distributional solutions are considered. Finally, numerical examples of realistic tunnel data with single and multiple solutions of the stationary problem are given. Copyright © 2003 John Wiley & Sons, Ltd. [source] Computational homogenization of uncoupled consolidation in micro-heterogeneous porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2010Fredrik Larsson Abstract Variationally consistent homogenization is exploited for the analysis of transient uncoupled consolidation in micro-heterogeneous porous solids, whereby the classical approach of first-order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are introduced in quadrature points in standard fashion. Along with the classical averages, a higher-order conservation quantity is obtained. An iterative FE2 -algorithm is devised for the case of nonlinear permeability and storage coefficients, and it is applied to pore pressure changes in asphalt-concrete (particle composite). Various parametric studies are carried out, in particular, with respect to the influence of the ,substructure length scale' that is represented by the size of the RVE's. Copyright © 2009 John Wiley & Sons, Ltd. [source] Variationally consistent computational homogenization of transient heat flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Fredrik Larsson Abstract A framework for variationally consistent homogenization, combined with a generalized macro-homogeneity condition, is exploited for the analysis of non-linear transient heat conduction. Within this framework the classical approach of (model-based) first-order homogenization for stationary problems is extended to transient problems. Homogenization is then carried out in the spatial domain on representative volume elements (RVE), which are (in practice) introduced in quadrature points in standard fashion. Along with the classical averages, a higher order conservation quantity is obtained. An iterative FE2 -algorithm is devised for the case of non-linear diffusion and storage coefficients, and it is applied to transient heat conduction in a strongly heterogeneous particle composite. Parametric studies are carried out, in particular with respect to the influence of the ,internal length' associated with the second-order conservation quantity. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||