International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 751-758

On weak solutions of semilinear hyperbolic-parabolic equations

Jorge Ferreira

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 (K1(x,t)u)+K2(x,t)u+A(t)u+F(u)=f with null Dirichlet boundary conditions and zero initial data, where F(s) is a continuous function such that sF(s)0, sR and {A(t);t0} is a family of operators of L(H01(Ω);H1(Ω)). For the 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 F.