Global and blow-up solutions for quasilinear parabolic equations with a gradient term and nonlinear boundary flux

Abstract

Abstract This work is concerned with positive classical solutions for a quasilinear parabolic equation with a gradient term and nonlinear boundary flux. We find sufficient conditions for the existence of global and blow-up solutions. Moreover, an upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’ and an upper estimate of the global solution are given. Finally, some application examples are presented. MSC:35R45, 35K65, 34A12.</jats:p