On weak solutions of semilinear hyperbolic-parabolic equations
Open Access
- 1 January 1996
- journal article
- research article
- Published by Hindawi Limited in International Journal of Mathematics and Mathematical Sciences
- Vol. 19 (4), 751-758
- https://doi.org/10.1155/s0161171296001044
Abstract
In this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equationwith null Dirichlet boundary conditions and zero initial data, whereis a continuous function such that,andis a family of operators of. 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.