International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 751-758
On weak solutions of semilinear hyperbolic-parabolic equations
Departamento de Matemática, Universidade Estadual de Maringá, Agência Postal UEM, Maringá 87020-900, PR, Brazil
Received 12 February 1993; Revised 15 December 1995
Copyright © 1996 Jorge Ferreira. 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 prove the existence and uniqueness of weak solutions of the mixed
problem for the nonlinear hyperbolic-parabolic equation
with null Dirichlet boundary conditions and
zero initial data, where is a continuous function such
that , and is a family of operators of .
existence we apply the Faedo-Galerkin method with
an unusual a priori estimate and a result of
W. A. Strauss. Uniqueness is proved only for some
particular classes of functions .