This article establishes the controllability to the trajectories of a reaction-diffusion-advection system describing predator-prey model by using distributed controls acting on a single equation with the no-flux boundary conditions. We first prove the exact null controllability of an associated linearized problem by establishing an observability estimate, derived from a global Carleman type inequality, for the adjoint system. The proof of the nonlinear problem relies on the suitable regularity of the control and Kakutani's fixed point theorem.
All Science Journal Classification (ASJC) codes
- Signal Processing
- Computer Science Applications
- Control and Optimization