Fractional heat equation with singular nonlinearity

Our aim in this paper is to analyze the existence and regularity of solutions for the following nonlocal parabolic problem involving the fractional Laplacian with singular nonlinearity {[ u_t+(-Δ )^s u =f(x,t)/u^γ in Ω _T:=Ω× (0,T),; u =0 in (ℝ^N\Ω )× (0,T),; u(· ,0) =u_0(· ) in Ω , ]. where Ω is a bounded domain of class 𝒞^0,1 in ℝ^N , N>2s with s∈ (0,1) , γ >0 , 0更多