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.
Bibliographical noteFunding Information:
Received 19 February 2010; Revised and Accepted 11 May 2010. K.S.’s work was supported by the Brain Korea 21 Project at Yonsei University, 2008. J.-H.K.’s work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund; KRF-2008-314-C00045). Address correspondence to K. Sakthivel, Department of Mathematics, Yonsei University, Seoul 120 749, Korea; E-mail: email@example.com
All Science Journal Classification (ASJC) codes
- Signal Processing
- Computer Science Applications
- Control and Optimization