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Published in:
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2019 | OriginalPaper | Chapter

Wave Equations in Modulation Spaces–Decay Versus Loss of Regularity

Authors : Maximilian Reich, Michael Reissig

Published in: New Tools for Nonlinear PDEs and Application

Publisher: Springer International Publishing

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Abstract

Recently the study of partial differential equations in modulation spaces gained some relevance. A well-known Cauchy problem is that for the wave equation, where several contributions exist concerning the local (in time) well-posedness. We refer to Bényi et al. (J Func Anal 246.2:366–384, 2007), Cordero and Nicola (J Math Anal Appl 353.2:583–591, 2009) and Reich (Modulation spaces and nonlinear partial differential equations. PhD thesis, TU Bergakademie Freiberg, 2017). By taking advantage of some tools and concepts from the theory of partial differential equations the authors provide some time-dependent estimates of the solution u = u(t, x) to the Cauchy problem of the free wave equation. The main result yields the possibility to consider more delicate problems concerning the wave equation in modulation spaces such as global (in time) well-posedness results.

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previous chapter Global Existence Results for a Semilinear Wave Equation with Scale-Invariant Damping and Mass in Odd Space Dimension
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Metadata
Title
Wave Equations in Modulation Spaces–Decay Versus Loss of Regularity
Authors
Maximilian Reich
Michael Reissig
Copyright Year
2019
Book
New Tools for Nonlinear PDEs and Application

Print ISBN: 978-3-030-10936-3

Electronic ISBN: 978-3-030-10937-0

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-10937-0_13

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