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Blow-up of Solutions to Semilinear Wave Equations with a Time-dependent Strong Damping by Fino, Ahmad Z.; Hamza, Mohamed is a scholarly article available to read on EtoBox.

What is Blow-up of Solutions to Semilinear Wave Equations with a Time-dependent Strong Damping about?

The paper investigates a class of a semilinear wave equation with time-dependent damping term ($-\frac{1}{{(1+t)}^{\beta}}\Delta u_t$) and a nonlinearity $|u|^p$. We will show the influence of the the parameter $\beta$ in the blow-up results under some hypothesis on the initial data and the exponent $p$ by using the test function method. We also study the local existence in time of mild solution in the energy space $H^1(\mathbb{R}^n)\times L^2(\mathbb{R}^n)$.

Author

Fino, Ahmad Z.; Hamza, Mohamed

Published

2021

Language

EN