On a Higher-order Reaction-diffusion Equation with a Special Medium Void via Potential Well Method

Abstract

Let d ∈ {1, 2, 3, . . .} and Ω ⊂ R d be open bounded with Lipschitz boundary. Consider the reaction-diffusion parabolic problemwhere T > 0, p ∈ (1, ∞), 0 = u 0 ∈ H 2 0 (Ω) and ν is the outward normal vector to ∂Ω. We investigate the existence of a global weak solution to the problem together with the decaying and blow-up properties using the potential well method.