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Quasi-symmetrizer and Hyperbolic Equations

  • Giovanni TaglialatelaEmail author
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 44)

Abstract

Given a matrix A, a symmetrizer for A is a symmetric matrix \(\mathcal{Q} \) such that \(\mathcal{Q} A\) is symmetric. The symmetrizer is a useful tool to obtain a-priori estimates for the solutions to hyperbolic equations. If \(\mathcal{Q}\) is not positive definite, it is more convenient to consider a quasi-symmetrizer: a sequence of symmetric and positive defined matrices \(\{\mathcal{Q}_{\varepsilon}\}_{\varepsilon\in]0,1 ]}\) such that \(\mathcal{Q}_{\varepsilon} A\) approaches a symmetric matrix.

In these notes we make a short survey of the basic notions of symmetrizer and quasi-symmetrizer and we give some applications to the well-posedness for the hyperbolic Cauchy problem.

Keywords

Cauchy problem Hyperbolic equations Symmetrizer 

Mathematics Subject Classification

35L30 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Dipartimento di Scienze Economiche e Metodi MatematiciUniversitá di BariBariItaly

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