具有wick -多项式非线性的随机演化方程

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2023-03-10 DOI:10.1214/18-EJP241

T. Levajković, S. Pilipovic, D. Seleši, M. Zigic

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引用次数: 5

摘要

我们在白噪声分析的框架下研究了具有Wick幂和Wick多项式型非线性集的非线性抛物型随机偏微分方程。这些方程包括随机Fujita方程、随机Fisher KPP方程和随机FitzHugh Nagumo方程等。通过将$C_0-$半群和演化系统的理论应用到无穷维空间中的混沌展开理论中，我们证明了这类SPDE解的存在性和唯一性。特别地，我们还处理了线性非自治情况，并提供了在生物学、医学和物理学中出现的随机反应扩散方程的几个应用。

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Stochastic evolution equations with Wick-polynomial nonlinearities

We study nonlinear parabolic stochastic partial differential equations with Wick-power and Wick-polynomial type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fujita equation, the stochastic Fisher-KPP equation and the stochastic FitzHugh-Nagumo equation among many others. By implementing the theory of $C_0-$semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove existence and uniqueness of solutions for this class of SPDEs. In particular, we also treat the linear nonautonomous case and provide several applications featured as stochastic reaction-diffusion equations that arise in biology, medicine and physics.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.