On weak solutions of semilinear hyperbolic‐parabolic equations
Open Access
- 15 December 1995
- journal article
- research article
- Published by Wiley 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 equation urn:x-wiley:01611712:media:ijmm289648:ijmm289648-math-0001 with null Dirichlet boundary conditions and zero initial data, where F(s) is a continuous function such that sF(s) ≥ 0, ∀s ∈ R and {A(t); t ≥ 0} is 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 F.Keywords
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