Advances in Differential Equations

Weak solutions to the Cauchy problem of a semilinear wave equation with damping and source terms

Petronela Radu

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Abstract

In this paper we prove local existence of weak solutions for a semilinear wave equation with power-like source and dissipative terms on the entire space $\mathbb R^n$. The main theorem gives an alternative proof of the local in time existence result due to J. Serrin, G. Todorova and E. Vitillaro, and also some extension to their work. In particular, our method shows that sources that are not locally Lipschitz in $L^2$ can be controlled without any damping at all. If the semilinearity involving the displacement has a "good" sign, we obtain global existence of solutions.

Article information

Source
Adv. Differential Equations Volume 10, Number 11 (2005), 1261-1300.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867752

Mathematical Reviews number (MathSciNet)
MR2175336

Zentralblatt MATH identifier
1195.35217

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35D05 35L15: Initial value problems for second-order hyperbolic equations

Citation

Radu, Petronela. Weak solutions to the Cauchy problem of a semilinear wave equation with damping and source terms. Adv. Differential Equations 10 (2005), no. 11, 1261--1300. https://projecteuclid.org/euclid.ade/1355867752.


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