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.