Blowup for a Fourth-Order Parabolic Equation with Gradient Nonlinearity

Abstract

Let $u$ be a solution to the Cauchy problem for a fourth-order nonlinear parabolic equation $\partial_t u+(-\Delta)^2u=-\nabla\cdot(|\nabla u|^{p-2}\nabla u)$ on ${\bf R}^N$, where $p>2$ and $N\ge ...