Stability criteria for parabolic type partial difference equations

This paper is concerned with the stability of neutral parabolic type partial difference equations with delays over cylin-drical domains (see (1.1), (1.4) and (3.1)). Stability criteria involving the spatial Euclidean norms of the solutions are derived by means of basic analytic techniques. These criteria will likely find applications in the stability of finite difference schemes resulting from discretising parabolic reaction diffusion equations.