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arXiv · 2404.16173

The lifespan of solutions of semilinear wave equation with weighted nonlinearity

Lulwah Al-Essa·Mohamed Majdoub
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Abstract

We investigate the lifespan of solutions to a specific variant of the semilinear wave equation, which incorporates weighted nonlinearity $$ u_{tt}-u_{xx} =|x|^\alpha |u|^p, \quad\mbox{for}\;\;\; (t,x)\in (0,\infty)\times\mathbb{R}, $$ where $p>1$, $\alpha\in\mathbb{R}$. We explore the behavior of solutions for small initial data, considering the influence of weighted nonlinearities on the lifespan.

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Lulwah Al-Essa, Mohamed Majdoub. 2024-04-24. The lifespan of solutions of semilinear wave equation with weighted nonlinearity. https://arxiv.org/abs/2404.16173

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