Asymptotic behavior of solutions to the multidimensional semidiscrete diffusion equation

Abstract

We study the asymptotic behavior of solutions to the multidimensional diffusion (heat) equation with continuous time and discrete space. We focus on initial-value problems with bounded initial data, and provide sufficient conditions for the existence of pointwise and uniform limits of solutions.

Keywords

• semidiscrete diffusion equation
• lattice diffusion equation
• modified Bessel function