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On pseudosymmetric hyperbolic systems. (English) Zbl 1014.35055

The authors investigate first-order weakly hyperbolic systems of PDEs with coefficients depending only on \(t\). The system is supposed to be pseudosymmetric according to a given definition (e.g., in two space dimensions, the system with the matrix \(A=(a_{ij})\) is pseudosymmetric iff \(a_{ii}\) are real and \(a_{12} \cdot a_{21} >0)\). Well-possedness of the Cauchy problem in \(H^\infty\) resp. in Gevrey classes is proved for the case of analytic resp. \(C^\infty\) coefficients.
Reviewer: A.Doktor (Praha)

MSC:

35L45 Initial value problems for first-order hyperbolic systems
35B65 Smoothness and regularity of solutions to PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

well-possedness
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References:

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