Study of a fractional stochastic heat equation

In this article, we study a d-dimensional stochastic nonlinear heat equation (SNLH) with quadratic nonlinearity, forced by fractional space-time white noise: ∂ t u − ∆u = ρ 2 +Ḃ , ∈ [0, T ] x R d 0 φ. Two types of regimes are exhibited, depending on the ranges Hurst index H (H ..., d) (0, 1) d+1. particular, show that local well-posedness resulting from Da Prato-Debussche trick, is easily obtained when 2H + i=1 i > d. On contrary, much more difficult to handle ≤ case, model has be interpreted in Wick sense, thanks time-dependent renormalization. Helped regularising effect semigroup, establish results for all dimension ≥ 1. Contents