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arXiv · 2404.12088

The inhomogeneous fractional stochastic heat equation driven by fractional Brownian motion

R. Alessa·R. Al Subaie·M. Alwohaibi·M. Majdoub·E. Mliki
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Abstract

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.

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R. Alessa, R. Al Subaie, M. Alwohaibi, M. Majdoub, E. Mliki. 2025-06-11. The inhomogeneous fractional stochastic heat equation driven by fractional Brownian motion. https://arxiv.org/abs/2404.12088

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