Self-similar solutions for the 2-D Burgers system in infinite subsonic channels
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 29-37
https://doi.org/10.4134/BKMS.2010.47.1.29
Printed January 1, 2010
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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