Self-similar Solutions of 2-D Compressible Euler Equations And Mixed-type Problems
Vol. 10 No. 3 (2015) P.393~P.421
The Riemann problem has been proved to play the role of building blocks in vari-
ous aspects of theory, numerics and applications of one-dimensional conservation laws. In
contrast, the solution structures of two-dimensional Riemann problems are much poorly
understood due to the instantaneous space-time interaction of nonlinear waves which
leads to complex but fascinating wave structures. These structures have the universal
self-similarity feature that reflects the invariant property under dilation. With the self-similarity reduction, the underlying problems change from the purely hyperbolic type to the hyperbolic-elliptic mixed type. In this paper we will formulate and review precisely some mathematical problems with plausible explicit structures in the construction of 2-D Riemann problems and propose some doable problems.
Hyperbolic conservation laws, compressible Euler equations, 2-D Riemann problems, self-similar solutions, mixed-type problems.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35L02, 35M10, 35M30, 76H05.
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Revised : 2015-05-30