Positivity for large time of solutions of the heat equation: The parabolic antimaximum principle

Abstract

We study the positivity, for large time, of the solutions to the heat equation Q(a) (f,u(0)): [GRAPHIC] where Q is a smooth bounded domain in RN and a C R. We obtain some sufficient conditions for having a finite time t(p) > 0 (depending on a and on the data u(0) and f which are not necessarily of the same sign) such that u(t, x) > 0 For Allt > t(p), a.e.x is an element of Omega.