Abstract
We prove local existence of a solution to a Riemann problem for the two-dimensional nonlinear wave system using the approach by Čanić, Keyfitz, Kim and Lieberman. We consider initial data resulting in weak regular shock reflection. By writing the problem in self-similar coordinates, we obtain a mixed type system and a free boundary problem for the subsonic flow and the position of the reflected shock. We reformulate this problem using a second order equation for density with mixed boundary conditions and an ordinary differential equation describing the location of the reflected shock. The main difficulty in the study of this second order problem for density is that the operator is degenerate elliptic along the sonic circle. We regularize and modify the operator, and we show existence of solutions to the regularized problems. We prove that the sequence of solutions to the regularized problems is precompact, and, using uniform local ellipticity, covering and diagonalization techniques, we obtain a local solution to the original problem.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.