Shock reflection for the damped -system

Authors:
Ling Hsiao and Hailiang Li

Journal:
Quart. Appl. Math. **60** (2002), 437-460

MSC:
Primary 35L60; Secondary 35B40, 35L55, 35L67, 76L05, 76S05

DOI:
https://doi.org/10.1090/qam/1914435

MathSciNet review:
MR1914435

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Abstract | References | Similar Articles | Additional Information

Abstract: The global existence and the asymptotic behavior of the weak entropy solution, the piecewise smooth solution with one shock discontinuity, on a strip domain is investigated in the present paper. We show that, for small smooth initial data and boundary value with only one small jump at , the piecewise smooth solution with one shock discontinuity exists globally in time. The shock discontinuity begins from , moves forward and reflects in a finite time at the boundary to form a 1-shock, which goes backward and reflects at also in a finite time to create a new 2-shock. The shock strength decays exponentially and never disappears in finite time. As , this solution converges to a constant state determined by the initial and the boundary conditions.

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DOI:
https://doi.org/10.1090/qam/1914435

Article copyright:
© Copyright 2002
American Mathematical Society