International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 533-548

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

Copyright © 1998 Haroldo R. Clark. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we consider the Cauchy problem {u+M(|A12u|2)Au=0in]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.