ABSTRACT
Free boundary problems deal with systems of partial differential equations, where a part of the domain boundary is unknown. This chapter only focuses on free boundary problems from ecological models. The main content includes the existence and uniqueness, regularity and uniform estimates of solutions, longtime behaviour of solutions, criteria and dichotomy for spreading and vanishing, and the asymptotic speed of the free boundary. It analyses longtime behaviours of criteria for spreading and vanishing, and spreading-vanishing dichotomy. Regularity and uniform estimates are important elements in the study of parabolic partial differential equations. They will be used to study long-time behaviour of solutions and to determine dichotomy for spreading and vanishing.
