Stochastic evolution equations with Wick-analytic nonlinearities

Abstract

We study nonlinear stochastic partial differential equations with Wick-analytic type nonlinearities set in the framework of white noise analysis. These equations include the stochastic Fisher–KPP equations, stochastic Allen–Cahn, stochastic Newell–Whitehead–Segel, and stochastic Fujita–Gelfand equations. By implementing the theory of $C_0-$semigroups and evolution systems into the chaos expansion theory in infinite dimensional spaces, we prove the existence and uniqueness of solutions for this class of stochastic partial differential equations.

Keywords:

• Weighted Hida spaces
• stochastic nonlinear evolution equations
• Wick product
• $C_0-$semigroup
• infinitesimal generator

Mathematics Subject Classifications:

• 60H15
• 60H40
• 60G20
• 37L55
• 47J35

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

S. Pilipović was supported by the Serbian Academy of Sciences and Arts under Grant No. F10. D. Seleši and M. Žigić gratefully acknowledge the financial support by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia under Grant No. 451–03–66/2024–03/200125 & 451–03–65/2024–03/200125. M. Žigić was supported by the Science Fund of the Republic of Serbia, $\mathrm{\#}$GRANT No 2727, Global and local analysis of operators and distributions - GOALS.