International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 505-520
A non-linear hyperbolic equation
Instituto de Matemática, UFRJ, Caixa Postal 1835, ZC-00, Rio de Janeiro, RJ, Brazil
Received 10 January 1979
Copyright © 1980 Eliana Henriques de Brito. 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 the following Cauchy problem, in a Hilbert space , is considered:
and are given functions, an operator in , satisfying convenient hypothesis, and is a real number.
For in the domain of and in the domain of , if , and in , when , a theorem of existence and uniqueness of weak solution is proved.