Advances in Differential Equations
- Adv. Differential Equations
- Volume 10, Number 11 (2005), 1261-1300.
Weak solutions to the Cauchy problem of a semilinear wave equation with damping and source terms
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.
Adv. Differential Equations Volume 10, Number 11 (2005), 1261-1300.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35D05 35L15: Initial value problems for second-order hyperbolic equations
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