The initial value problem for stochastic reaction-diffusion equations with continuous reaction

Abstract

We give general conditions for existence and uniqueness of mild solutions to the initial value problem for stochastic reaction-diffusion equations with an additive (i.e. state-independent) noise which is coloured in space and white in time. The method represented here analogously works in the space-time white noise case. We essentially make use of a growth estimate for continuous random fields which helps to establish a Banach space in which the solution lives

Keywords:

• Stochastic Reaction-Diffusion Equation
• Stochastic Integral
• Generalized Random Field
• Growth of Random Functions
• Comparison theorem