Asymptotic behavior of solutions to the semidiscrete diffusion equation

Abstrakt

We study the asymptotic behavior of bounded solutions to the one-dimensional diffusion (heat) equation with discrete space and continuous time. We show that a bounded solution approaches the average of the initial values if the average exists, and provide estimates in the situation when it does not exist.

Klíčová slova

• Semidiscrete diffusion equation
• Lattice diffusion equation
• Modified Bessel function