The lifespan of solutions of semilinear wave equation with weighted nonlinearity
Authors
Lulwah Al-Essa, Mohamed Majdoub
Categories
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
Categories
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
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