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The lifespan of solutions of semilinear wave equation with weighted nonlinearity

Published 1 year agoVersion 3arXiv:2404.16173

Authors

Lulwah Al-Essa, Mohamed Majdoub

Categories

math.AP

Abstract

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

The lifespan of solutions of semilinear wave equation with weighted nonlinearity

1 year ago
v3
2 authors

Categories

math.AP

Abstract

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

Authors

Lulwah Al-Essa, Mohamed Majdoub

arXiv ID: 2404.16173
Published Apr 24, 2024

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