International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 505-520

A non-linear hyperbolic equation

Eliana Henriques de Brito

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 H, is considered: (I+λA)u+A2u+[α+M(|A12u|2)]Au=fu(0)=u0u(0)=u1

M and f are given functions, A an operator in H, satisfying convenient hypothesis, λ0 and α is a real number.

For u0 in the domain of A and u1 in the domain of A12, if λ>0, and u1 in H, when λ=0, a theorem of existence and uniqueness of weak solution is proved.