Finite time blow-up and global existence of solutions for semilinear parabolic equations with nonlinear dynamical boundary condition

Abstract

<p style='text-indent:20px;'>For a class of semilinear parabolic equations under nonlinear dynamical boundary conditions in a bounded domain, we obtain finite time blow-up solutions when the initial data varies in the phase space <inline-formula><tex-math id="M1">$ H_0^1(\Omega) $</tex-math></inline-formula> at positive initial energy level and get global solutions with the initial data at low and critical energy level. Our main tools are potential well method and concavity method.</p>