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2018 Stochastic evolution equations with Wick-polynomial nonlinearities
Tijana Levajković, Stevan Pilipović, Dora Seleši, Milica Žigić
Electron. J. Probab. 23: 1-25 (2018). DOI: 10.1214/18-EJP241

Abstract

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.

Citation

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Tijana Levajković. Stevan Pilipović. Dora Seleši. Milica Žigić. "Stochastic evolution equations with Wick-polynomial nonlinearities." Electron. J. Probab. 23 1 - 25, 2018. https://doi.org/10.1214/18-EJP241

Information

Received: 8 June 2018; Accepted: 30 October 2018; Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 07021672
MathSciNet: MR3885549
Digital Object Identifier: 10.1214/18-EJP241

Subjects:
Primary: 11B83, 37L55, 47J35, 60G20, 60H15, 60H40

JOURNAL ARTICLE
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Vol.23 • 2018
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