Exponential stabilization of periodic solutions of a system of KdV equations
Summary: We consider a coupled nonlinear dispersive system of Korteweg-de Vries type in the presence of a dissipative mechanism. First we prove that the Cauchy problem is globally well posed in a suitable periodic Sobolev space and our main result says that the \(L^{2}\) and \(L^{\infty }\) norms of the solutions decay exponentially fast as \(t \rightarrow + \infty \).
scientific article; zbMATH DE number 5554819