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July/August 2014 Existence, uniqueness, and analyticity of space-periodic solutions to the regularized long-wave equation
R. Chertovskih, A.C.L. Chian, O. Podvigina, E.L. Rempel, V. Zheligovsky
Adv. Differential Equations 19(7/8): 725-754 (July/August 2014).

Abstract

We consider space-periodic evolutionary and travelling-wave solutions to the regularized long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and smoothness of the evolutionary solutions for smooth initial conditions, and global in time spatial analyticity of such solutions for analytical initial conditions. The width of the analyticity strip decays at most polynomially. We prove existence of travelling-wave solutions and uniqueness of travelling waves of a sufficiently small norm. The importance of damping is demonstrated by showing that the problem of finding travelling-wave solutions to the undamped RLWE is not well-posed. Finally, we demonstrate the asymptotic convergence of the power series expansion of travelling waves for a weak forcing.

Citation

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R. Chertovskih. A.C.L. Chian. O. Podvigina. E.L. Rempel. V. Zheligovsky. "Existence, uniqueness, and analyticity of space-periodic solutions to the regularized long-wave equation." Adv. Differential Equations 19 (7/8) 725 - 754, July/August 2014.

Information

Published: July/August 2014
First available in Project Euclid: 6 May 2014

zbMATH: 1292.35227
MathSciNet: MR3252900

Subjects:
Primary: 35A01, 35A02, 35C07, 35Q35, 35Q51

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.19 • No. 7/8 • July/August 2014
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