Publications in Scientific Journals:
T. Levajković, S. Pilipovic, D. Selesi, M. Zigic:
"Stochastic evolution equations with Wick-polynomial nonlinearities";
Electronic Journal of Probability,
23
(2018),
116
- 140.
English 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 C0−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.
Keywords:
Hida-Kondratiev spaces, stochastic nonlinear evolution equations, Wick product, infinitesimal generator
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1214/18-EJP241
Electronic version of the publication:
https://publik.tuwien.ac.at/files/publik_276615.pdf
Created from the Publication Database of the Vienna University of Technology.