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New Tools for Nonlinear PDEs and Application

  • Book
  • © 2019

Overview

Editors:
  1. Marcello D'Abbicco

    1. Mathematics, University of Bari, Bari, Italy

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  2. Marcelo Rempel Ebert

    1. Department of Computing and Mathematics, University of São Paulo, Ribeirão Preto, Brazil

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    You can also search for this editor in PubMed   Google Scholar

  3. Vladimir Georgiev

    1. Department of Mathematics, University of Pisa, Pisa, Italy

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    You can also search for this editor in PubMed   Google Scholar

  4. Tohru Ozawa

    1. Department of Applied Physics, Waseda University, Tokyo, Japan

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  • Contains thirteen papers devoted to recent results in mathematics, focusing on nonlinear partial differential equation and applications
  • Provides contributions about qualitative properties of solutions of linear and nonlinear models, well-posedness results, results on asymptotic profiles of solutions, on blow-up behavior and on the influence of low regular coefficients

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-viii
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  2. On Effective PDEs of Quantum Physics

    • Ilias Chenn, I. M. Sigal
    Pages 1-47

  3. Critical Exponents for Differential Inequalities with Riemann-Liouville and Caputo Fractional Derivatives

    • Marcello D’Abbicco
    Pages 49-95

  4. Weakly Coupled Systems of Semilinear Effectively Damped Waves with Different Time-Dependent Coefficients in the Dissipation Terms and Different Power Nonlinearities

    • Abdelhamid Mohammed Djaouti, Michael Reissig
    Pages 97-128

  5. Incompressible Limits for Generalisations to Symmetrisable Systems

    • Michael Dreher
    Pages 129-151

  6. The Critical Exponent for Evolution Models with Power Non-linearity

    • Marcelo Rempel Ebert, Linniker Monteiro Lourenço
    Pages 153-177

  7. Blow-Up or Global Existence for the Fractional Ginzburg-Landau Equation in Multi-dimensional Case

    • Luigi Forcella, Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa
    Pages 179-202

  8. Semilinear Damped Klein-Gordon Models with Time-Dependent Coefficients

    • Giovanni Girardi
    Pages 203-216

  9. Wave-Like Blow-Up for Semilinear Wave Equations with Scattering Damping and Negative Mass Term

    • Ning-An Lai, Nico Michele Schiavone, Hiroyuki Takamura
    Pages 217-240

  10. 4D Semilinear Weakly Hyperbolic Wave Equations

    • Sandra Lucente
    Pages 241-261

  11. Smoothing and Strichartz Estimates to Perturbed Magnetic Klein-Gordon Equations in Exterior Domain and Some Applications

    • Kiyoshi Mochizuki, Sojiro Murai
    Pages 263-280

  12. The Cauchy Problem for Dissipative Wave Equations with Weighted Nonlinear Terms

    • Makoto Nakamura, Hidemitsu Wadade
    Pages 281-303

  13. Global Existence Results for a Semilinear Wave Equation with Scale-Invariant Damping and Mass in Odd Space Dimension

    • Alessandro Palmieri
    Pages 305-369

  14. Wave Equations in Modulation Spaces–Decay Versus Loss of Regularity

    • Maximilian Reich, Michael Reissig
    Pages 371-390
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Keywords

About this book

This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.


Editors and Affiliations

  • Mathematics, University of Bari, Bari, Italy

    Marcello D'Abbicco

  • Department of Computing and Mathematics, University of São Paulo, Ribeirão Preto, Brazil

    Marcelo Rempel Ebert

  • Department of Mathematics, University of Pisa, Pisa, Italy

    Vladimir Georgiev

  • Department of Applied Physics, Waseda University, Tokyo, Japan

    Tohru Ozawa

Bibliographic Information

  • Book Title: New Tools for Nonlinear PDEs and Application

  • Editors: Marcello D'Abbicco, Marcelo Rempel Ebert, Vladimir Georgiev, Tohru Ozawa

  • Series Title: Trends in Mathematics

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

  • Publisher: Birkhäuser Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-10936-3Published: 08 May 2019

  • eBook ISBN: 978-3-030-10937-0Published: 07 May 2019

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: VIII, 390

  • Number of Illustrations: 1 b/w illustrations, 5 illustrations in colour

  • Topics: Partial Differential Equations

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