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.
Author: | Irina Kmit |
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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 |