Remarks on blow-up phenomena in p-Laplacian heat equation with inhomogeneous nonlinearity

Eadah Ahmad Alzahrani; Mohamed Majdoub

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arXiv · 2006.11311

Remarks on blow-up phenomena in p-Laplacian heat equation with inhomogeneous nonlinearity

Eadah Ahmad Alzahrani·Mohamed Majdoub

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Abstract

We investigate the $p-$Laplace heat equation $u_t-\Delta_p u=\zeta(t)f(u)$ on a bounded smooth domain $\Omega\subset\mathbb{R}^N$. Using differential inequalities arguments, we prove blow-up results under suitable conditions on $\zeta, f$, and the initial data $u_0$. We also give an upper bound for the blow-up time in each case.

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Eadah Ahmad Alzahrani, Mohamed Majdoub. 2020-06-19. Remarks on blow-up phenomena in p-Laplacian heat equation with inhomogeneous nonlinearity. https://arxiv.org/abs/2006.11311

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