Bulletin of the
Korean Mathematical Society
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ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Self-similar solutions for the 2-D Burgers system in infinite subsonic channels

Kyungwoo Song

Kyung Hee University

Abstract

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

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