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Smoothing effect and Fredholm property for first-order hyperbolic PDEs

Please always quote using this URN:urn:nbn:de:0296-matheon-11946
  • We give an exposition of recent results on regularity and Fredholm properties for first-order one-dimensional hyperbolic PDEs. We show that large classes of boundary operators cause an effect that smoothness increases with time. This property is the key in finding regularizers (parametrices) for hyperbolic problems. We construct regularizers for periodic problems for dissipative first-order linear hyperbolic PDEs and show that these problems are modeled by Fredholm operators of index zero.

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Metadaten
Author:Irina Kmit
URN:urn:nbn:de:0296-matheon-11946
Referee:Alexander Mielke
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/02/08
Release Date:2013/02/08
Tag:first-order hyperbolic systems, initial-boundary problems; time-periodic solutions, regularity of solutions; Fredholm solvability
Institute:Humboldt-Universität zu Berlin
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L04 Initial-boundary value problems for first-order hyperbolic equations
Preprint Number:997
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