Hyperbolic equations, function spaces with exponential weights and Nemytskij operators |
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Authors: | Gé rard Bourdaud, Michael Reissig Winfried Sickel |
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Affiliation: | (1) Euipe dAnalyse Fonctionnelle, Université Pierre et Marie Curie, Case 186, 4 place Jussieu, 75252 Paris Cedex 05, France;(2) Institut für Angewandte Mathematik I, TU Bergakademie Freiberg, Agricolastrasse 1, D-09596 Freiberg, Germany;(3) Mathematisches Institut, FSU Jena, Ernst-Abbe-Platz 1–4, D-07743 Jena, Germany |
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Abstract: | Different problems in the theory of hyperbolic equations bases on function spaces of Gevrey type are studied. Beside the original Gevrey classes, spaces defined by the behaviour of the Fourier transform were also used to prove basic results about the well-posedness of Cauchy problems for non-linear hyperbolic systems. In these approaches only the algebra property of the function spaces was used to include analytic non-linearities. Here we will generalize this dependence. First we investigate superposition operators in spaces with exponential weights. Then we show in concrete situations how a priori estimates of strictly hyperbolic type lead to the well-posedness of certain semi-linear hyperbolic Cauchy problems in suitable function spaces with exponential weights of Gevrey type. Mathematics Subject Classification (2000) 46E35, 35L80, 35L15, 47H30 |
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Keywords: | Nemytskij operators function spaces with exponential weights Gevrey classes hyperbolic equations |
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