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Birkhäuser

Phase Space Analysis of Partial Differential Equations

  • Book
  • © 2007

Overview

Editors:
  1. Antonio Bove

    1. Dipartimento di Matematica, Università di Bologna, Bologna, Italy

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  2. Ferruccio Colombini

    1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

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    You can also search for this editor in PubMed   Google Scholar

  3. Daniele Santo

    1. Dipartimento di Scienze Matematiche, Università di Trieste, Trieste, Italy

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  • Covers phase space analysis methods, including microlocal analysis, and their applications to physics
  • Treats the linear and nonnlinear aspects of the theory of PDEs
  • Original articles are self-contained with full proofs; survey articles give a quick and direct introduction to selected topics evolving at a fast pace
  • Excellent reference and resource for grad students and researchers in PDEs and related fields

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 69)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Trace theorem on the Heisenberg group on homogeneous hypersurfaces

    • Hajer Bahouri, Jean-Yves Chemin, Chao-Jiang Xu
    Pages 1-15

  3. Strong unique continuation and finite jet determination for Cauchy-Riemann mappings

    • M. Salah Baouendi
    Pages 17-28

  4. On the Cauchy problem for some hyperbolic operator with double characteristics

    • Enrico Bernardi, Antonio Bove
    Pages 29-44

  5. On the differentiability class of the admissible square roots of regular nonnegative functions

    • Jean-Michel Bony, Ferruccio Colombini, Ludovico Pernazza
    Pages 45-53

  6. The Benjamin—Ono equation in energy space

    • Nicolas Burq, Fabrice Planchon
    Pages 55-62

  7. Instabilities in Zakharov equations for laser propagation in a plasma

    • Thierry Colin, Guy Métivier
    Pages 63-81

  8. Symplectic strata and analytic hypoellipticity

    • Paulo D. Cordaro, Nicholas Hanges
    Pages 83-94

  9. On the backward uniqueness property for a class of parabolic operators

    • Daniele Del Santo, Martino Prizzi
    Pages 95-105

  10. Inverse problems for hyperbolic equations

    • Gregory Eskin
    Pages 107-116

  11. On the optimality of some observability inequalities for plate systems with potentials

    • Xiaoyu Fu, Xu Zhang, Enrique Zuazua
    Pages 117-132

  12. Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach

    • Peter W. Michor
    Pages 133-215

  13. Non-effectively hyperbolic operators and bicharacteristics

    • Tatsuo Nishitani
    Pages 217-246

  14. On the Fefferman-Phong inequality for systems of PDEs

    • Alberto Parmeggiani
    Pages 247-266

  15. Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations

    • Vesselin Petkov
    Pages 267-285

  16. An elementary proof of Fediĭ’s theorem and extensions

    • David S. Tartakoff
    Pages 287-290

  17. Outgoing parametrices and global Strichartz estimates for Schrödinger equations with variable coefficients

    • Daniel Tataru
    Pages 291-313

  18. On the analyticity of solutions of sums of squares of vector fields

    • François Treves
    Pages 315-329
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Keywords

About this book

This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theory.

Key topics:

* The Cauchy problem for linear and nonlinear hyperbolic equations

* Scattering theory

* Inverse problems

* Hyperbolic systems

* Gevrey regularity of solutions of PDEs

* Analytic hypoellipticity

and unique features:

* Original articles are self-contained with full proofs

* Survey articles give a quick and direct introduction to selected topics evolving at a fast pace

Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource.

Editors and Affiliations

  • Dipartimento di Matematica, Università di Bologna, Bologna, Italy

    Antonio Bove

  • Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Ferruccio Colombini

  • Dipartimento di Scienze Matematiche, Università di Trieste, Trieste, Italy

    Daniele Santo

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