In this talk, we will review some explosive models from combustion theory. These models do not satisfy global Lipschitz condition in general, therefore nonexistence or multiplicity of classic solution are of extensive interests. We shall study a class of generalized explosive model with extremely low order temporal fractional derivative. Blowup phenomenon is theoretically analyzed and numerical simulation is carried out via a mixed numerical method based on adaptive finite difference and discontinuous Galerkin method. It is shown that the size of spatial domain cannot be too small, for guaranteeing the appearance of explosion of solution, which coincides with the physical observation.
Prof. Xu is an associate professor of School of Mathematics and Statistics, Central South University, China. He got his PhD degree in Central South University in 2014. His research area include finite difference method and finite element methods for solving nonlinear fractional PDEs.