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

Abstract EN

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.