Evolution Equations of Hyperbolic and Schrödinger Type

1. Front Matter

   Pages i-viii

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2. Divergence-type Operators: Spectral Theory and Spacetime Estimates

   • Matania Ben-Artzi

   Pages 1-40

3. Kinetic Models of Chemotaxis

   • Nikolaos Bournaveas, Vincent Calvez

   Pages 41-52

4. Modulus of Continuity and Decay at Infinity in Evolution Equations with Real Characteristics

   • Massimo Cicognani, Ferruccio Colombini

   Pages 53-62

5. Time-Frequency Analysis of Schrödinger Propagators

   • Elena Cordero, Fabio Nicola, Luigi Rodino

   Pages 63-85

6. Geometric Regularization on Riemannian and Lorentzian Manifolds

   • Shantanu Dave, Günther Hörmann, Michael Kunzinger

   Pages 87-102

7. A Remark on the Uniqueness for Backward Parabolic Operators with non-Lipschitz-continuous Coefficients

   • Daniele Del Santo

   Pages 103-114

8. Dispersive Properties of Schrödinger Operators in the Absence of a Resonance at Zero Energy in 3D

   • Vladimir Georgiev, Mirko Tarulli

   Pages 115-143

9. Decay Estimates for the Supercritical 3-D Schrödinger Equation with Rapidly Decreasing Potential

   • Vladimir Georgiev, Bozhidar Velichkov

   Pages 145-162

10. Wave Equations on Non-smooth Space-times

    • Günther Hörmann, Michael Kunzinger, Roland Steinbauer

    Pages 163-186

11. Lower Bounds for the Lifespan of Solutions to Nonlinear Wave Equations in Elasticity

    • Hideo Kubo

    Pages 187-212

12. Representation Formula of the Resolvent for Wave Equation with a Potential Outside the Convex Obstacle

    • Tokio Matsuyama

    Pages 213-225

13. On the Scattering on a Loop-shaped Graph

    • K. Mochizuki, I. Yu. Trooshin

    Pages 227-245

14. On the Cauchy Problem for Hyperbolic Operators with Double Characteristics

    • Cesare Parenti, Alberto Parmeggiani

    Pages 247-266

15. Modulation Spaces and Nonlinear Evolution Equations

    • Michael Ruzhansky, Mitsuru Sugimoto, Baoxiang Wang

    Pages 267-283

16. An Optimal Control Problem for a Nonlinear Hyperbolic Equation with an Infinite Time Horizon

    • Simon Serovajsky, Kanat Shakenov

    Pages 285-300

17. Local in Space Energy Estimates for Second-order Hyperbolic Equations

    • Sergio Spagnolo, Giovanni Taglialatela

    Pages 301-313

18. The Final Problem on the Optimality of the General Theory for Nonlinear Wave Equations

    • Hiroyuki Takamura, Kyouhei Wakasa

    Pages 315-324

Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions  and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area. ​

• Schrödinger equations
• generalized functions
• hyperbolic equations
• partial differential equations
• pseudo-differential operators

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

  Michael Ruzhansky

• , Graduate School of Mathematics, Nagoya University, Nagoya, Japan

  Mitsuru Sugimoto

• , Fachbereich Mathematik, Universität Stuttgart, Stuttgart, Germany

  Jens Wirth

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