Solutions to a 3D Burgers Equation with Initial Discontinuity That Are Two Disjoint Spheres

Solutions to a 3D Burgers Equation with Initial Discontinuity That Are Two Disjoint Spheres

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

Author Details

Shu Wang

Niu Haiping