ON SOME DECAY ESTIMATES OF SOLUTIONS FOR SOME NONLINEAR DEGENERATE DIFFUSION EQUATIONS

Abstract:

We consider the existence and some decay estimates of solutions of the following initial boundary value problem for some nonlinear degenerate parabolic equations:

Here u(x,t) is a scalar function of the spatial variable x(∈ Ω) and time t(> 0), and Ω is a regular bounded domain in R^N (N > 2) with the smooth boundary ∂Ω, R⁺ = (0,+∞), Δ denotes the N-dimensional Laplace operator, m > 1, p > 0, and f(x,t) and u₀(x) satisfy some hypotheses which will be given later.