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 problem where T > 0, p ∈ (1 , ∞ ), 0 (cid:54) = u 0 ∈ H 20 (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.