Resumen de Global and blow-up solutions for nonlinear parabolic equations with a gradient term

Juntang Ding, Bao-Zhu Guo

• In this paper, we are concerned with the a kind of nonlinear parabolic equations with a gradient term and Neumann boundary condition in a bounded domain in N-dimensional Euclidean space with smooth boundary. The upper and lower solution technique is adopted in investigations. The sufficient conditions for the existence of global positive solution and an upper estimate of global solution are given. Moreover, under some appropriate assumptions on the coefficients functions, we prove the existence of blow-up positive solution. An upper bound of �blow-up time� is also presented