Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation

Siva Athreya, Oleg Butkovsky, Khoa Lê +1

We study stochastic reaction--diffusion equation $${\partial }_t{u}_t(x)=\frac{1}{2}{\partial }_{xx}^2{u}_t(x)+b(u_t(x))+{\dot{W}}_t(x),t>0,x\in D$$ where $b$ is a generalized funct…