Invariant measure of stochastic higher order KdV equation driven by Poisson processes

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2021-08-23 DOI:10.1051/MMNP/2021041

Pengfei Xu, Jianhua Huang, Wei Yan

引用次数: 2

Abstract

The current paper is devoted to stochastic damped higher order KdV equation driven by Poisson process. We establish the well-posedness of stochastic damped higher-order KdV equation, and prove that there exists an unique invariant measure for non-random initial conditions. Some discussion on the general pure jump noise case are also provided. Some numerical simulations of the invariant measure are provided to support the theoretical results. Mathematics Subject Classification. 60H15, 37L55. Received March 27, 2020. Accepted July 13, 2021.

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泊松过程驱动的随机高阶KdV方程的不变测度

本文研究了泊松过程驱动的随机阻尼高阶KdV方程。建立了随机阻尼高阶KdV方程的适定性，并证明了对于非随机初始条件存在唯一不变测度。对一般纯跳变噪声情况也作了讨论。给出了一些不变测度的数值模拟来支持理论结果。数学学科分类。60H15, 37L55。收于2020年3月27日。2021年7月13日接受。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

5.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.