Description
This talk analyzes the Korteweg-de Vries-Burgers (KdV-Burgers) equation on the negative half-line, \R^-. We present results on well-posedness in H^s(\R^-) for s\ge-1 and boundary controllability. New boundary estimates for solutions of the KdV-Burgers equation on \R^- are obtained. The unbounded domain \R^- introduces challenges to compactness properties crucial for proving exact controllability, necessitating a review of the intrinsic properties of the equation.
Références:
-Bona, J., Sun, S., \& Zhang, B.-Y. (2008). Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equation in a quarter plane. Ann. I. H. Poincar\'e-AN, 25, 1145–1185.
-Rosier, L. (2000). Exact Boundary Controllability for the Linear Korteweg--de Vries Equation on the Half-Line. SIAM Journal on Control and Optimization, 39(2), 331–351.
-Esquivel L. Rivas I. Well-posedness and Bounded controllability for the Korteweg-de Vries-Burger equation in a half-plane. Submitted.
