Exact Null Controllability of KdV-Burgers Equation with Memory Effect Systems

Abstract

This paper is concerned with exact null controllability analysis of nonlinear KdV-Burgers equation with memory. The proposed approach relies upon regression tool to prove controllability property of linearized KdV-Burgers equation via Carleman estimates. The control is distributed along with subdomain $\omega \subset \Omega$ and the external control acts on the key role of observability inequality with memory. This description finally showed the exact null controllability guaranteeing the stability.