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Stochastic evolution equations with Wick-polynomial nonlinearities. (English) Zbl 1406.60096
Summary: 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.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H40 White noise theory
60G20 Generalized stochastic processes
37L55 Infinite-dimensional random dynamical systems; stochastic equations
47J35 Nonlinear evolution equations
11B83 Special sequences and polynomials
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