Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

Abstract

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee that u(x,t) exists globally or blows up at some finite time t*. Moreover, an upper bound for t* is derived. Under somewhat more restrictive conditions, a lower bound for t* is also obtained.