The inhomogeneous fractional stochastic heat equation driven by fractional Brownian motion
We investigate the fractional Hardy-Hénon equation with fractional Brownian noise $$ \partial_tu(t)+(-Δ)^{θ/2} u(t)=|x|^{-γ} |u(t)|^{p-1}u(t)+μ\, \partial_t B^H(t), $$ where $θ>0$, $p>1$, $γ\geq 0$, $μ\in\mathbb{R}$, and the random forcing $B^H$ is the fractional Brownian motion defined on some complete probability space $(Ω, \mathcal{F}, \mathbb{P})$ with Hurst parameter $H\in (0,1)$. We establish the local existence and uniqueness of mild solutions under appropriate conditions on the parameters of the equation.
math.AP↗