Reaction-Diffusion Equations with Polynomial Drifts Driven by Fractional Brownian Motions

Abstract

A reaction-diffusion equation on [0, 1] ^d with the heat conductivity κ > 0, a polynomial drift term and an additive noise, fractional in time with H > 1/2, and colored in space, is considered. We have shown the existence, uniqueness and uniform boundedness of solution with respect to κ. Also we show that if κ tends to infinity, then the corresponding solutions of the equation converge to a process satisfying a stochastic ordinary differential equation.

Keywords:

• Fractional Brownian motion
• Polynomial drift
• Reaction-diffusion equation

Mathematics Subject Classification:

• 60H15
• 60G18