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
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.
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.