Global Existence And Blow-up Phenomena For Two Class Nonlinear Heat Equations

In chapter two, we consider inhomogeneous Neumann boundary problem of p-Laplacian heat equation We establish the conditions on f and g to guarantee that u(x,t) exists globally or blows up at some finite time, respectively. If blow-up occurs, we obtain the upper and lower bounds of the blow-up time by differential inequalities.In chapter three, we consider inhomogeneous Neumann boundary problem of non-linear divergence form parabolic equation We establish the conditions on nonlinearities and aij to guarantee that u(x,t) exists globally or blows up at some finite time, respectively. If blow-up occurs, we obtain the upper and lower bounds of the blow-up time by Sobolev type inequality and some related inequalities.