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Progress in Partial Differential Equations

Asymptotic Profiles, Regularity and Well-Posedness

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Michael Reissig

    1. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

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  2. Michael Ruzhansky

    1. Department of Mathematics, Imperial College London, London, United Kingdom

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    You can also search for this editor in PubMed   Google Scholar

  • Contains survey and research articles
  • Provides an excellent introduction to special research topics
  • Suited for graduate students and researchers at various levels
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 44)

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Table of contents (18 papers)

  1. Front Matter

    Pages I-VIII
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  2. Global Existence and Energy Decay of Solutions for a Nondissipative Wave Equation with a Time-Varying Delay Term

    • Abbes Benaissa, Salim A. Messaoudi
    Pages 1-26

  3. Non-uniqueness and Uniqueness in the Cauchy Problem of Elliptic and Backward-Parabolic Equations

    • Daniele Del Santo, Christian P. Jäh
    Pages 27-52

  4. On Internal Regularity of Solutions to the Initial Value Problem for the Zakharov–Kuznetsov Equation

    • A. V. Faminskii, A. P. Antonova
    Pages 53-74

  5. Singular Semilinear Elliptic Equations with Subquadratic Gradient Terms

    • Marius Ghergu
    Pages 75-91

  6. On the Parabolic Regime of a Hyperbolic Equation with Weak Dissipation: The Coercive Case

    • Marina Ghisi, Massimo Gobbino
    Pages 93-123

  7. H ∞ Well-Posedness for Degenerate p-Evolution Models of Higher Order with Time-Dependent Coefficients

    • Torsten Herrmann, Michael Reissig, Karen Yagdjian
    Pages 125-151

  8. On the Global Solvability for Semilinear Wave Equations with Smooth Time Dependent Propagation Speeds

    • Fumihiko Hirosawa, Takuhiro Inooka, Trieu Duong Pham
    Pages 153-181

  9. Filippov Solutions to Systems of Ordinary Differential Equations with Delta Function Terms as Summands

    • Uladzimir Hrusheuski
    Pages 183-200

  10. Resolvent Estimates and Scattering Problems for Schrödinger, Klein-Gordon and Wave Equations

    • Kiyoshi Mochizuki
    Pages 201-221

  11. On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data

    • Alexey Nikitin
    Pages 223-238

  12. Critical Exponent for the Semilinear Wave Equation with Time or Space Dependent Damping

    • Kenji Nishihara
    Pages 239-259

  13. A Note on a Class of Conservative, Well-Posed Linear Control Systems

    • Rainer Picard, Sascha Trostorff, Marcus Waurick
    Pages 261-286

  14. Recent Progress in Smoothing Estimates for Evolution Equations

    • Michael Ruzhansky, Mitsuru Sugimoto
    Pages 287-302

  15. Differentiability of Inverse Operators

    • Simon Y. Serovajsky
    Pages 303-320

  16. Solution of the Cauchy Problem for Generalized Euler-Poisson-Darboux Equation by the Method of Fractional Integrals

    • A. K. Urinov, S. T. Karimov
    Pages 321-337

  17. Quasi-symmetrizer and Hyperbolic Equations

    • Giovanni Taglialatela
    Pages 339-366

  18. Thermo-elasticity for Anisotropic Media in Higher Dimensions

    • Jens Wirth
    Pages 367-407

  19. Global Solutions of Semilinear System of Klein-Gordon Equations in de Sitter Spacetime

    • Karen Yagdjian
    Pages 409-444

  20. Back Matter

    Pages 445-447
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Keywords

About this book

Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society.

This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The readers will find this an excellent resource of both introductory and advanced material. The key topics are:

• Linear hyperbolic equations and systems (scattering, symmetrisers)
• Non-linear wave models (global existence, decay estimates, blow-up)
• Evolution equations (control theory, well-posedness, smoothing)
• Elliptic equations (uniqueness, non-uniqueness, positive solutions)
• Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)

Editors and Affiliations

  • Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  • Department of Mathematics, Imperial College London, London, United Kingdom

    Michael Ruzhansky

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