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Decay rates for the solutions of model equations for bore propagation

Published online by Cambridge University Press:  14 November 2011

S. V. Rajopadhye
S. V. Rajopadhye
Affiliation:
Department of Mathematics, University of California, Santa Cruz, CA 95064, U.S.A.
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Abstract

We study the large-time behaviour of solutions to the Korteweg-de Vries-Burgers equation with bore-like initial data. This work relies on the methods of Amick, Bona and Schonbeck to obtain sharp rates of temporal decay of certain norms of the solution, thus obtaining an improvement over results of Naumkin and Shishmarev.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 2 , 1995 , pp. 371 - 398
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Amick, C. J., Bona, J. L. and Schonbek, M. E.. Decay of solutions of some nonlinear wave equations. J. Differential Equations 81 (1989), 1–49.CrossRefGoogle Scholar
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3Bona, J. L., Rajopadhye, S. V. and Schonbek, M. E.. Model equations for the propagation of bores I. Two-dimensional theory. Differential and Integrated Equations 7 (1994), 699–734.CrossRefGoogle Scholar
4Naumkin, P. I. and Shishmarëv, I. A.. On the decay of a step for the K-dV-Burgers equation, Methods in the theory of singular perturbations in applied problems (Paper presented at the Riga conference on singular perturbation theory, 1990).Google Scholar