On the Fujita exponent for a nonlinear parabolic equation with a forcing term

Abstract

The purpose of this work is to analyze the blow-up of solutions of the nonlinear parabolic equation \[ u_t-Δu=|x|^α|u|^{p}+{\mathtt a}(t)\textbf{w}(x) \ \quad\mbox{for } (t,x)\in(0,\infty)\times\mathbb{R}^{N}, \] where $p>1$, $\alpha \in \mathbb{R}$ and $\mathtt{a}$, $\text{w}$ are suitable given functions. We improve earlier results by considering a wide class of functions $\mathtt{a}(t)$.

arXiv commentA revised version will be prepared