Long-time behaviour of solutions of a non-linear diffusion problem with non-local source term
P. Shi, Meng Wang · IMA Journal of Applied Mathematics · 2010
This paper is devoted to the long-time behaviour of solutions for the Dirichlet problem of the non-local porous medium equation for the case f(u) = a + up with m > p ≥ 1, λ, q > 0 and a > 0. We first prove the existence and uniqueness of the solution of the associated steady-state problem. Then, for the non-negative initial data u0(x) satisfying and u0 = 0 on ∂Ω, we discuss the asymptotic stability of the unique steady-state solution and the estimate of the convergence rate, at last we give the numerical simulations.