Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation
| dc.creator | Coclite, G. C. | |
| dc.creator | Karlsen, K. H. | |
| dc.creator | Kwon, Y. -S. | |
| dc.date | 2008-11-04 | |
| dc.date.accessioned | 2026-07-07T10:15:26Z | |
| dc.date.available | 2026-07-07T10:15:26Z | |
| dc.description | 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. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0811.0549 | |
| dc.identifier | http://arxiv.org/abs/0811.0549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173172 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L65, 35G25 | |
| dc.title | Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation | |
| dc.type | text |