ON THE BLOW-UP SOLUTIONS TO A FOURTH-ORDER PSEUDO-PARABOLIC EQUATION WITH GRADIENT NON-LINEARITY

Abstract

In this note, the initial and periodic boundary value problem
was solved for the following fourth-order pseudo-parabolic equation
with gradient non-linearity and pseudo term
u_t − aΔu_t − Δu + Δ^2u = −∇ · (|∇u|^(p−2)∇u)
where a ≥ 0. Local existence-uniqueness result for mild solutions was
found for any initial data in L2(Ω). In addition, the existence of blowup
solutions was proved and a lower bound for the blow-up time was
obtained.