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## Linear Partial Differential Equations (linear + partial_differential_equation)
## Selected Abstracts## THE DIFFUSIVE SPREAD OF ALLELES IN HETEROGENEOUS POPULATIONS EVOLUTION, Issue 3 2004Garrick T. SkalskiAbstract The spread of genes and individuals through space in populations is relevant in many biological contexts. I study, via systems of reaction-diffusion equations, the spatial spread of advantageous alleles through structured populations. The results show that the temporally asymptotic rate of spread of an advantageous allele, a kind of invasion speed, can be approximated for a class of linear partial differential equations via a relatively simple formula, c= 2,rD, that is reminiscent of a classic formula attributed to R. A. Fisher. The parameters r and D, represent an asymptotic growth rate and an average diffusion rate, respectively, and can be interpreted in terms of eigenvalues and eigenvectors that depend on the population's demographic structure. The results can be applied, under certain conditions, to a wide class of nonlinear partial differential equations that are relevant to a variety of ecological and evolutionary scenarios in population biology. I illustrate the approach for computing invasion speed with three examples that allow for heterogeneous dispersal rates among different classes of individuals within model populations. [source] ## A review of reliable numerical models for three-dimensional linear parabolic problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007I. FaragóAbstract The preservation of characteristic qualitative properties of different phenomena is a more and more important requirement in the construction of reliable numerical models. For phenomena that can be mathematically described by linear partial differential equations of parabolic type (such as the heat conduction, the diffusion, the pricing of options, etc.), the most important qualitative properties are: the maximum,minimum principle, the non-negativity preservation and the maximum norm contractivity. In this paper, we analyse the discrete analogues of the above properties for finite difference and finite element models, and we give a systematic overview of conditions that guarantee the required properties a priori. We have chosen the heat conduction process to illustrate the main concepts, but engineers and scientists involved in scientific computing can easily reformulate the results for other problems too. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Part 2: Neumann boundary conditionsAbstract We present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound-hard scatterer. We apply this method to the solution of a mock-up submarine problem, and highlight its computational advantages and intrinsic parallelism. A key component of our method is an original idea for addressing a Neumann boundary condition in the general framework of a fictitious domain method. This idea is applicable to many other linear partial differential equations besides the Helmholtz equation. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Opérateurs différentiels linéaires à coefficients constants et schémas de Hilbert ponctuels MATHEMATISCHE NACHRICHTEN, Issue 5 2008Jean D'AlmeidaAbstract We use algebraic methods to study systems of linear partial differential equations with constant coefficients. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Homogenization in the Theory of Viscoplasticity PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Sergiy NesenenkoWe study the homogenization of the quasistatic initial boundary value problem with internal variables which models the deformation behavior of viscoplastic bodies with a periodic microstructure. This problem is represented through a system of linear partial differential equations coupled with a nonlinear system of differential equations or inclusions. Recently it was shown by Alber [2] that the formally derived homogenized initial boundary value problem has a solution. From this solution we construct an asymptotic solution for the original problem and prove that the difference of the exact solution and the asymptotic solution tends to zero if the lengthscale of the microstructure goes to zero. The work is based on monotonicity properties of the differential equations or inclusions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] |