Electronic Journal of Probability
- Electron. J. Probab.
- Volume 23 (2018), paper no. 116, 25 pp.
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.
Electron. J. Probab., Volume 23 (2018), paper no. 116, 25 pp.
Received: 8 June 2018
Accepted: 30 October 2018
First available in Project Euclid: 24 November 2018
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Digital Object Identifier
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H40: White noise theory 60G20: Generalized stochastic processes 37L55: Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25] 11B83: Special sequences and polynomials
Levajković, Tijana; Pilipović, Stevan; Seleši, Dora; Žigić, Milica. Stochastic evolution equations with Wick-polynomial nonlinearities. Electron. J. Probab. 23 (2018), paper no. 116, 25 pp. doi:10.1214/18-EJP241. https://projecteuclid.org/euclid.ejp/1543028704