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

• Tipo: Artigo em Revista Científica Internacional
• Data: 2014

Autores

Chertovskih, R (Autor) Outra; Chian, ACL (Autor) Outra; Podvigina, O (Autor) Outra; Rempel, EL (Autor) Outra; Zheligovsky, V (Autor) Outra

Revista

Título: Advances in Differential Equations

Vol. 19

Páginas: 725-754

ISSN: 1079-9389

Editora: Khayyam Publishing, Inc.

Indexação

ISI Web of Knowledge - 2 Citações

Scopus - 2 Citações

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 30