On weak solutions of semilinear hyperbolic‐parabolic equations

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 s F ( 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 .

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