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Mathematics of Wave Phenomena

  • Conference proceedings
  • © 2020

Overview

Editors:
  1. Willy Dörfler

    1. Karlsruhe Institute of Technology, Karlsruhe, Germany

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  2. Marlis Hochbruck

    1. Karlsruhe Institute of Technology, Karlsruhe, Germany

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  3. Dirk Hundertmark

    1. Karlsruhe Institute of Technology, Karlsruhe, Germany

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  4. Wolfgang Reichel

    1. Karlsruhe Institute of Technology, Karlsruhe, Germany

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  5. Andreas Rieder

    1. Karlsruhe Institute of Technology, Karlsruhe, Germany

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  6. Roland Schnaubelt

    1. Karlsruhe Institute of Technology, Karlsruhe, Germany

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  7. Birgit Schörkhuber

    1. Karlsruhe Institute of Technology, Karlsruhe, Germany

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  • Provides a comprehensive overview of current state-of-the-art by renowned experts
  • Contains a unique combination of perspectives from analysis, numerics, inverse problems and selected applications
  • Deals with aspects of mathematics of wave phenomena

Part of the book series: Trends in Mathematics (TM)

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Table of contents (20 papers)

  1. Front Matter

    Pages i-viii
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  2. Morawetz Inequalities for Water Waves

    • Thomas Alazard, Mihaela Ifrim, Daniel Tataru
    Pages 1-14

  3. Numerical Study of Galerkin–Collocation Approximation in Time for the Wave Equation

    • Mathias Anselmann, Markus Bause
    Pages 15-36

  4. Effective Numerical Simulation of the Klein–Gordon–Zakharov System in the Zakharov Limit

    • Simon Baumstark, Guido Schneider, Katharina Schratz
    Pages 37-48

  5. Exponential Dichotomies for Elliptic PDE on Radial Domains

    • Margaret Beck, Graham Cox, Christopher Jones, Yuri Latushkin, Alim Sukhtayev
    Pages 49-68

  6. Stability of Slow Blow-Up Solutions for the Critical Focussing Nonlinear Wave Equation on \(\mathbb {R}^{3+1}\)

    • Stefano Burzio
    Pages 69-88

  7. Local Well-Posedness for the Nonlinear Schrödinger Equation in the Intersection of Modulation Spaces \(M_{p, q}^s({\mathbb {R}}^d) \cap M_{\infty , 1}({\mathbb {R}}^d)\)

    • Leonid Chaichenets, Dirk Hundertmark, Peer Christian Kunstmann, Nikolaos Pattakos
    Pages 89-107

  8. FEM-BEM Coupling of Wave-Type Equations: From the Acoustic to the Elastic Wave Equation

    • Sarah Eberle
    Pages 109-124

  9. On Hyperbolic Initial-Boundary Value Problems with a Strictly Dissipative Boundary Condition

    • Matthias Eller
    Pages 125-144

  10. On the Spectral Stability of Standing Waves of Nonlocal \(\mathcal {P}\mathcal {T}\) Symmetric Systems

    • Wen Feng, Milena Stanislavova
    Pages 145-162

  11. Sparse Regularization of Inverse Problems by Operator-Adapted Frame Thresholding

    • Jürgen Frikel, Markus Haltmeier
    Pages 163-178

  12. Soliton Solutions for the Lugiato–Lefever Equation by Analytical and Numerical Continuation Methods

    • Janina Gärtner, Wolfgang Reichel
    Pages 179-195

  13. Error Analysis of Discontinuous Galerkin Discretizations of a Class of Linear Wave-type Problems

    • Marlis Hochbruck, Jonas Köhler
    Pages 197-218

  14. Ill-posedness of the Third Order NLS with Raman Scattering Term in Gevrey Spaces

    • Nobu Kishimoto, Yoshio Tsutsumi
    Pages 219-233

  15. Invariant Measures for the DNLS Equation

    • Renato Lucà
    Pages 235-242

  16. A Global div-curl-Lemma for Mixed Boundary Conditions in Weak Lipschitz Domains

    • Dirk Pauly
    Pages 243-250

  17. Existence and Stability of Klein–Gordon Breathers in the Small-Amplitude Limit

    • Dmitry E. Pelinovsky, Tiziano Penati, Simone Paleari
    Pages 251-278

  18. On Strichartz Estimates from ℓ 2-Decoupling and Applications

    • Robert Schippa
    Pages 279-289

  19. On a Limiting Absorption Principle for Sesquilinear Forms with an Application to the Helmholtz Equation in a Waveguide

    • Ben Schweizer, Maik Urban
    Pages 291-307

  20. Some Inverse Scattering Problems for Perturbations of the Biharmonic Operator

    • Valery Serov
    Pages 309-325
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Keywords

About this book

Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics.

The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

Editors and Affiliations

  • Karlsruhe Institute of Technology, Karlsruhe, Germany

    Willy Dörfler, Marlis Hochbruck, Dirk Hundertmark, Wolfgang Reichel, Andreas Rieder, Roland Schnaubelt, Birgit Schörkhuber

Bibliographic Information

  • Book Title: Mathematics of Wave Phenomena

  • Editors: Willy Dörfler, Marlis Hochbruck, Dirk Hundertmark, Wolfgang Reichel, Andreas Rieder, Roland Schnaubelt, Birgit Schörkhuber

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-47174-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-47173-6Published: 02 October 2020

  • Softcover ISBN: 978-3-030-47176-7Published: 03 October 2021

  • eBook ISBN: 978-3-030-47174-3Published: 01 October 2020

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: VIII, 327

  • Number of Illustrations: 4 b/w illustrations, 16 illustrations in colour

  • Topics: Partial Differential Equations, Numerical Analysis

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