The Fujita Exponent for Semilinear Heat Equations with Quadratically Decaying Potential or in an Exterior Domain

Ross G. Pinsky

Consider the equation u_t=Δu-Vu +au^p \text{in} R^n\times (0,T); u(x,0)=ϕ(x)\gneq0, \text{in} R^n, where $p>1$, $n\ge 2$, $T\in (0,\infty ]$, $V(x)\sim \frac{\omega }{|x{|}^2}$ as $|x|\to \infty$…