  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.
