Stabilization for degenerate diffusion with absorption Original Research Article

The purpose of this paper is to study the limit in L1(Ω) of solutions of general initial-boundary-value problems of the form ut=Δw−g(x,u) and u∈β(w) in a bounded domain Ω with general boundary conditions of the form ∂ηw+γ(w)∋0, where β and γ are maximal monotone graphs and View the MathML source is a nonincreasing continuous function in View the MathML source. We prove that a solution stabilizes in L1(Ω) as t→∞ to a function View the MathML source which satisfies View the MathML source a.e. x∈Ω, with c∈γ−1(0). So, if for instance γ−1(0)=ϕ−1(0)∩g(x,.)−1(0)={0}, then a solution stabilizes by converging to 0, in L1(Ω), as t→∞