Abstract

In this paper we study the asymptotic behavior for a nonlocal heat equation in an inhomogenous medium: put = J * u - u in RN x, where p is a continuous positive function, u is non-negative and J is a probability measure having finite second-order momentum. Depending on integrability conditions on the initial data u0 and p, we prove various isothermalisation results, i.e. u converges to a constant state in the whole space