Year: 2017
Author: Shu Wang, Niu Haiping
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 3 : pp. 232–253
Abstract
We study the singular structure of a kind of three dimensional non-selfsimilar global solutions and their interaction for quasilinear hyperbolic conservation laws. The initial discontinuity is two disjoint unit spheres and initial data just contain two different constant states, the global solutions and some new phenomena are discovered. We give the solutions in 0 ‹ t ‹ T^* and T^* ‹ t, and at t=T^*, the two basic shock waves and the constant state u_ are disappeared.Then, we find a new shock wave between two rarefaction by R-H condition. Finally, we show the limit of the solution when t → ∞. A technique is proposed to construct the three dimensional shock wave without dimensional reduction or coordinate transformation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v30.n3.4
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 3 : pp. 232–253
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Initial discontinuity