Initial Boundary Value Problem of the General Three-Component Camassa-Holm Shallow Water System on an Interval

Abstract EN

We study the initial boundary value problem of the general three-component Camassa-Holm shallow water system on an interval subject to inhomogeneous boundary conditions.

First we prove a local in time existence theorem and present a weak-strong uniqueness result.

Then, we establish a asymptotic stabilization of this system by a boundary feedback.

Finally, we obtain a result of blow-up solution with certain initial data and boundary profiles.