Back to Search
Start Over
On a degenerate boundary value problem to the two-dimensional self-similar nonlinear wave system
- Source :
- Boundary Value Problems, Vol 2019, Iss 1, Pp 1-16 (2019)
- Publication Year :
- 2019
- Publisher :
- SpringerOpen, 2019.
-
Abstract
- Abstract This paper focuses on a degenerate boundary value problem arising from the study of the two-dimensional Riemann problem to the nonlinear wave system. In order to deal with the parabolic degeneracy, we introduce a partial hodograph transformation to transform the nonlinear wave system into a new system, which displays a clear regularity–singularity structure. The local existence of classical solutions for the new system is established in a weighted metric space. Returning the solution to the original variables, we obtain the existence of classical solutions to the degenerate boundary value problem for the nonlinear wave system.
Details
- Language :
- English
- ISSN :
- 16872770
- Volume :
- 2019
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Boundary Value Problems
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.9d0ffe16615f4cd19a1e9dd5e187af0c
- Document Type :
- article
- Full Text :
- https://doi.org/10.1186/s13661-018-1115-7