Bull. Korean Math. Soc. 2010; 47(1): 29-37
Printed January 1, 2010
https://doi.org/10.4134/BKMS.2010.47.1.29
Copyright © The Korean Mathematical Society.
Kyungwoo Song
Kyung Hee University
We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp.
Keywords: changing-type equations, degenerating quasilinear elliptic equations, self-similar solutions, 2-D full Euler equations
MSC numbers: 35J70, 35M10, 35L65
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd