Partial Differential Equations Arising from Physics and Geometry: A Volume in Memory of Abbas Bahri

doi:10.1017/9781108367639

In this edited volume leaders in the field of partial differential equations present recent work on topics in PDEs arising from geometry and physics. The papers originate from a 2015 research school organized by CIMPA and MIMS in Hammamet, Tunisia to celebrate the 60th birthday of the late Professor Abbas Bahri. The opening chapter commemorates his life and work. While the research presented in this book is cutting-edge, the treatment throughout is at a level accessible to graduate students. It includes short courses offering readers a unique opportunity to learn the state of the art in evolution equations and mathematical models in physics, which will serve as an introduction for students and a useful reference for established researchers. Finally, the volume includes many open problems to inspire the next generation.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
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Abbas Bahri: A Dedicated Life
pp ix-xvi
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1 - Blow-up Rate for a Semilinear Wave Equation with Exponential Nonlinearity in One Space Dimension
pp 1-32
- By Asma Azaiez, Nader Masmoudi, Hatem Zaag
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2 - On the Role of Anisotropy in the Weak Stability of the Navier–Stokes System
pp 33-87
- By Hajer Bahouri, Jean-Yves Chemin, Isabelle Gallagher
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3 - The Motion Law of Fronts for Scalar Reaction-diffusion Equations with Multiple Wells: the Degenerate Case
pp 88-171
- By Fabrice Bethuel, Didier Smets
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4 - Finite-time Blowup for some Nonlinear Complex Ginzburg–Landau Equations
pp 172-214
- By Thierry Cazenave, Seifeddine Snoussi
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5 - Asymptotic Analysis for the Lane–Emden Problem in Dimension Two
pp 215-252
- By Francesca De Marchis, Isabella Ianni, Filomena Pacella
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6 - A Data Assimilation Algorithm: the Paradigm of the 3D Leray-α Model of Turbulence
pp 253-273
- By Aseel Farhat, Evelyn Lunasin, Edriss S. Titi
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7 - Critical Points at Infinity Methods in CR Geometry
pp 274-295
- By Najoua Gamara
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8 - Some Simple Problems for the Next Generations
pp 296-310
- By Alain Haraux
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9 - Clustering Phenomena for Linear Perturbation of the Yamabe Equation
pp 311-331
- By Angela Pistoia, Giusi Vaira
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10 - Towards Better Mathematical Models for Physics
pp 332-454
- By Luc Tartar
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Partial Differential Equations Arising from Physics and Geometry

A Volume in Memory of Abbas Bahri

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Abbas Bahri: A Dedicated Life
pp ix-xvi

1 - Blow-up Rate for a Semilinear Wave Equation with Exponential Nonlinearity in One Space Dimension
pp 1-32

2 - On the Role of Anisotropy in the Weak Stability of the Navier–Stokes System
pp 33-87

3 - The Motion Law of Fronts for Scalar Reaction-diffusion Equations with Multiple Wells: the Degenerate Case
pp 88-171

4 - Finite-time Blowup for some Nonlinear Complex Ginzburg–Landau Equations
pp 172-214

5 - Asymptotic Analysis for the Lane–Emden Problem in Dimension Two
pp 215-252

6 - A Data Assimilation Algorithm: the Paradigm of the 3D Leray-α Model of Turbulence
pp 253-273

7 - Critical Points at Infinity Methods in CR Geometry
pp 274-295

8 - Some Simple Problems for the Next Generations
pp 296-310

9 - Clustering Phenomena for Linear Perturbation of the Yamabe Equation
pp 311-331

10 - Towards Better Mathematical Models for Physics
pp 332-454

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Partial Differential Equations Arising from Physics and Geometry

A Volume in Memory of Abbas Bahri

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