Extinction and decay estimates of solutions for a polytropic filtration equation with the nonlocal source and interior absorption

摘要

This paper deals with the extinction properties of solutions for the homogeneous Dirichlet boundary value problem with the nonlocal source and interior absorption ut=div(um|p-2um)+λ∫Ωuq(x,t)dx-kur,(x,t) ∈Ω×(0,∞), where m,λ,k,q > 0, 0 < m(p - 1) < 1, r ≤ 1, and Ω∩RN(N≥1). By using L~p-integral norm estimate method, we obtain the sufficient conditions of extinction solutions. Moreover, we also give the precise decay estimates of the extinction solutions.