Abstract:

In this talk we will introduce some fundamental upper and lower solution method in the study of partial differential equations (PDEs).

We will illustrate this method by using some classical PDEs, like the Laplace equation and heat equation. As for its applications, we will focus onthe reaction diffusion equations arising (RDs) from mathematical ecology, chemical reaction and network. Topics include the existence of solutions with general initial data, or some  traveling wave solutions, persistence and extinction for some species. Some recent results will be reported as well.

This talk will be presented at the level of Calculus.