Mathematica Eterna
Open Access

Abstract

Global and blow-up solutions for a quasilinear parabolic equation with different kinds boundary condition

Zhong Bo Fang, Rui Yang adn Lu Sun

We investigate a quasilinear parabolic equation with a gradient term subject to homogeneous Dirichlet or Neumann boundary condition. By constructing auxiliary functions and using Hopf’s maximum principle, we obtain the sufficient conditions for the existence of global and blowup solutions, the upper bounds for the “blow-up time”, the “upper estimates” of the “blow-up rate” and the “upper estimates” of the global solution. Finally, some application examples will be presented.