WEAK SOLUTIONS TO THE CAUCHY PROBLEM OF A SEMILINEAR WAVE EQUATION WITH DAMPING AND SOURCE TERMS

Authors

Petronela Radu, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

2005

Citation

Advances in Differential Equations Volume 10, Number 11 (2005), 1261–1300

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 ℝⁿ. 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 L² can be controlled without any damping at all. If the semilinearity involving the displacement has a “good” sign, we obtain global existence of solutions.