Multi-dimensional Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on admissible multi-dimensional domains

2022/05/22 by Nikolai A. Larkin, Larkin, Nikolai
Mathematics · #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2205.10832

Abstract

An initial-boundary value problem for the n-dimensional (n is a natural number from the interval [2,7]) Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on smooth bounded domains in ℝⁿ was considered. The existence and uniqueness of global regular solutions as well as their exponential decay have been established. A connection between an order of the stationary part of the equation and admissible dimensions of a domain has been revealed. Keywords: Kuramoto-Sivashinsky equation, Zakharov-Kuznetsov equation, Global solutions

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