Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation
Abstract
We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary condition. Equipped with this formulation, we go on to establish the well-posedness of entropy solutions to the initial-boundary value problem. The proof utilizes the kinetic formulation and the compensated compactness method. Finally, we make use of these results to demonstrate the well-posedness in a class of discontinuous solutions to the initial-boundary value problem for the Degasperis-Procesi shallow water equation, which is a third order nonlinear dispersive equation that can be rewritten in the form of a nonlinear conservation law with a nonlocal source term.
Cite
@article{arxiv.0811.0549,
title = {Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation},
author = {G. C. Coclite and K. H. Karlsen and Y. -S. Kwon},
journal= {arXiv preprint arXiv:0811.0549},
year = {2008}
}
Comments
24 pages