Large-Time Behavior of the Solutions to Rosenau-Type Approximations to the Heat Equation

In this article we study the large-time behavior of the solution to a general Rosenau type approximation to the heat equation [16], by showing that the solution to this approximation approaches the fundamental solution of the heat equation (the heat kernel), but at a slower rate than the usual heat equation. This result is valid in particular for the central differences scheme approximation of the heat equation, a property which to our knowledge has never been observed before.