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

Nikolai Larkin

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

Analysis of PDEs 2022-05-24 v1

Authors: Nikolai Larkin

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 $\mathbb{R}^n$ 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

Keywords

Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation initial-boundary value problem global regular solutions exponential decay admissible domains

Cite

@article{arxiv.2205.10832,
  title  = {Multi-dimensional Kuramoto-Sivashinsky-Zakharov-Kuznetsov equation posed on admissible multi-dimensional domains},
  author = {Nikolai Larkin},
  journal= {arXiv preprint arXiv:2205.10832},
  year   = {2022}
}

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arXiv admin note: text overlap with arXiv:2203.14739

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

Abstract

Keywords

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