Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions

Abstract

<abstract><p>In this paper, we consider an initial-boundary value parabolic problem under nonlinear Neumann boundary conditions. By virtue of the modified differential inequality, lower bounds for the blow-up time of the solution are derived in higher dimensional spaces. An upper bound for the blow-up time are specified under appropriate assumptions on the functions $ a, b, f, g, h $ and $ u_0 $.</p></abstract>