Frequently Hypercyclic and Chaotic Behavior of Some First-Order Partial Differential Equation

Abstract

We study a particular first-order partial differential equation which arisen from a biologic model. We found that the solution semigroup of this partial differential equation is a frequently hypercyclic semigroup. Furthermore, we show that it satisfies the frequently hypercyclic criterion, and hence the solution semigroup is also a chaotic semigroup.