EXISTENCE, UNIQUENESS, AND ANALYTICITY OF SPACE-PERIODIC SOLUTIONS TO THE REGULARIZED LONG-WAVE EQUATION

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Chertovskih, R (Author) Other; Chian, ACL (Author) Other; Podvigina, O (Author) Other; Rempel, EL (Author) Other; Zheligovsky, V (Author) Other

Journal

Title: Advances in Differential Equations

Vol. 19

Pages: 725-754

ISSN: 1079-9389

Publisher: Khayyam Publishing, Inc.

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 2 Citations

Other information

Authenticus ID: P-009-K4Y

Abstract (EN): 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 die undamped RLWE is not well-posed. Finally, we demonstrate the asymptotic convergence of the power series expansion of travelling waves for a weak forcing.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 30