Smoothing effect and Fredholm property for first-order hyperbolic PDEs

Details Smoothing effect and Fredholm property for first-order hyperbolic PDEs Smoothing effect and Fredholm property for first-order hyperbolic PDEs

2012-02-28

arxiv.org/abs/1202.6282v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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 they are modeled by Fredholm operators of index zero.

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