On admissibility for parabolic equations in R^n

Martino Prizzi

We consider the parabolic equation $$u_t-\Delta u=F(x,u),(t,x)\in {\mathbb{R}}_{+}\times {\mathbb{R}}^n\text{\hspace{1em}(P)}$$ and the corresponding semiflow $\pi$ in the phase space $H^1$. We give conditions on the nonl…