International Journal of Mathematics and Mathematical Sciences 
Volume 21 (1998), Issue 3, Pages 533-548
doi:10.1155/S016117129800074X

Global classical solutions to the Cauchy problem for a nonlinear wave equation

Haroldo R. Clark

 Universidade Federal Fluminense, Instituto de Matemática - GAN, Rua S. Paulo, 30, Niterói 24.040-110, RJ, Brazil
Received 24 August 1995; Revised 3 January 1997

Abstract

In this paper we consider the Cauchy problem {u″+M(|A12u|2)Au=0   in   ]0,T[u(0)=u0,       u′(0)=u1, where u′ is the derivative in the sense of distributions and |A12u| is the H-norm of A12u. We prove the existence and uniqueness of global classical solution.