BLOW-UP PHENOMENA FOR A QUASILINEAR PARABOLIC EQUATION WITH TIME-DEPENDENT COEFFICIENTS UNDER NONLINEAR BOUNDARY FLUX

This paper deals with blow-up phenomena for an initial boundary value problem of a quasilinear parabolic equation with time-dependent coeffcient in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and differential inequality technique, we establish some conditions on time-dependent coeffcient and nonlinear functions for which the solution u(x, t) exists globally or blows up at some finite time t*. Moreover, some upper and lower bounds for t* are derived in higher dimensional spaces. Some examples are presented to illustrate ap-plications of our results.