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2003, Volume 9, Issue 5: 1243-1262. Doi: 10.3934/dcds.2003.9.1243
This issue Previous Article A spectral characterization of exponential stability for linear time-invariant systems on time scales Next Article Generalized quasilinearization method for semilinear hyperbolic problems

Convergence to strong nonlinear rarefaction waves for global smooth solutions of $p-$system with relaxation

  • 1.

    Laboratory of Mathematical Physics, Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, P. O. Box 71010, Wuhan 430071

Received:  June 30, 2002
Revised:  November 30, 2002
Published:  August 2003
Abstract Related Papers Cited by
    Abstract
  • This paper is concerned with the large time behavior of global smooth solutions to the Cauchy problem of the $p-$system with relaxation. Former results in this direction indicate that such a problem possesses a global smooth solution provided that the first derivative of the solutions with respect to the space variable $x$ are sufficiently small. Under the same small assumption on the global smooth solution, we show that it converges to the corresponding nonlinear rarefaction wave and in our analysis, we do not ask the rarefaction wave to be weak and the initial error can also be chosen arbitrarily large.
    Mathematics Subject Classification: 35L45, 35L60.

    Citation:
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