| Abstract: | This paper deals with some homogeneous Dirichlet problems of nonlinear diffusion equations. After demonstrating the existence and uniqueness of weak solutions, we prove the existence and non-existence of global solutions. The influence of coefficients and geometry of domain is shown clearly on the existence of global solutions. We give the complete classification of simultaneous blow-up of solutions with blow-up rates as well in one-dimensional space. Moreover, the bounds of blow-up time are studied for all dimensions of space domain. |
