Rosenau Approximations

The research article Large-time behavior of the solutions to Rosenau type approximations to the heat equation, written in collaboration with Giuseppe Toscani, has been accepted for publication in SIAM J. App. Math. Super!

In this article we study the large-time behavior of the solution to a general Rosenau type approximation to the heat equation, 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.