The properties of blow-up of solutions to a porous medium equation including nonlinear nonlocal boundary condition

Abstract

In this paper, we consider the blow-up properties of the positive solutions to a porous medium equation u = Δum + c(x,t)up for (x,t) ∈ Ω × (0,∞) with nonlinear nonlocal boundary condition equations and nonnegative initial data where p > 0 and l > 0. We prove global existence theorem and the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data.