Existence and uniqueness of solutions to discrete diffusion equations
type: Item
instance of: scholarly article
title: Existence and uniqueness of solutions to discrete diffusion equations
zbMATH Open document ID: 1077.39014
DOI: 10.1016/S0898-1221(03)00087-7
author: Douglas R. Anderson
author: Richard I. Avery
author: John M. Davis
publication date: 2004-08-06T00:00:00Z
review text: The authors establish a formula for the unique solution of the nonhomogeneous discrete diffusion equation \[ \begin{aligned} \Delta_t u(x,t)-k\Delta^2_{x,x}u(x-1,t)&=f(x,t),\quad x\in\mathbb Z,\quad t\geq0,\\ u(x,0)&=\psi(x),\qquad x\in\mathbb Z, \end{aligned} \] where \(k\in(0,1)\). The key of the proof is the construction of the Green's function for the associated partial difference operator.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A05
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 2082216
zbMATH Keywords: partial difference equations
zbMATH Keywords: Green's function
zbMATH Keywords: discrete diffusion equation
reviewed by: Mihály Pituk
MaRDI profile type: Publication
cites work: Q4398858
cites work: Q4507789
cites work: Q4033029
cites work: Q4224851
cites work: Fundamental Solutions for Multivariate Difference Equations
cites work: Boundary value problems for partial difference equations
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 2082216