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

Abstract In this paper, we study the following degenerate parabolic problem: (0.1) ( P t ) { ∂ t u = Δ ϕ ( u ) + m ( x ) u  in  ( 0 , + ∞ ) × R n u ( t , x ) → | x | → + ∞ 0 ; u ( 0 , x ) = u 0 ( x )  in  R n where m is a continuous function which could be negative in a bounded set of R n and ϕ a C 1 convex increasing function. Under additive conditions, we prove the uniqueness of the positive stationary solution and, then, give the asymptotic behaviour of solutions to ( P t ) when t → + ∞ .