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arXiv · 2206.04930

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

A. Alshehri·N. Aljaber·H. Altamimi·M. Majdoub
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Abstract

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

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A. Alshehri, N. Aljaber, H. Altamimi, M. Majdoub. 2022-06-10. On the Fujita exponent for a nonlinear parabolic equation with a forcing term. https://arxiv.org/abs/2206.04930

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