In this paper, we establish the blow-up theorems of the Fujita type for a class of homogeneous Neumann problems of quasilinear equations with convection terms. The critical Fujita exponents are determined and it is shown that the exponents belong to the blow-up case under any nontrivial initial data. An interesting phenomenon is exploited such that the critical Fujita exponent even could be infinite for the model considered in the paper owing to the effect of convection.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.