Attractivity properties of nonnegative solutions for a degenerate parabolic equation in the whole space

In this paper, we study the following degenerate parabolic problem: equation(0.1)(Pt){∂tu=Δϕ(u)+m(x)u in (0,+∞)×Rnu(t,x)→|x|→+∞0;u(0,x)=u0(x) in Rn where mm is a continuous function which could be negative in a bounded set of RnRn and ϕϕ a C1C1 convex increasing function. Under additive conditions, we prove the uniqueness of the positive stationary solution and, then, give the asymptotic behaviour of solutions to (Pt)(Pt) when t→+∞t→+∞.