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.
In this edited volume leaders in the field of partial differential equations present recent work and current open problems on topics in PDEs arising from geometry and physics. It will serve as a useful reference for researchers and is written in a manner that is accessible to graduate students.
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Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.
| Preface |
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vii | |
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| Abbas Bahri: A Dedicated Life |
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ix | |
| 1 Blow-up Rate for a Semilinear Wave Equation with Exponential Nonlinearity in One Space Dimension |
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1 | (32) |
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| 2 On the Role of Anisotropy in the Weak Stability of the Navier-Stokes System |
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33 | (55) |
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| 3 The Motion Law of Fronts for Scalar Reaction-diffusion Equations with Multiple Wells: the Degenerate Case |
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88 | (84) |
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| 4 Finite-time Blowup for some Nonlinear Complex Ginzburg-Landau Equations |
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172 | (43) |
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| 5 Asymptotic Analysis for the Lane-Emden Problem in Dimension Two |
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215 | (38) |
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| 6 A Data Assimilation Algorithm: the Paradigm of the 3D Leray-a Model of Turbulence |
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253 | (21) |
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| 7 Critical Points at Infinity Methods in CR Geometry |
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274 | (22) |
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| 8 Some Simple Problems for the Next Generations |
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296 | (15) |
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| 9 Clustering Phenomena for Linear Perturbation of the Yamabe Equation |
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311 | (21) |
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| 10 Towards Better Mathematical Models for Physics |
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332 | |
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Mohamed Ben Ayed is Professor at the Université de Sfax, Tunisia. Mohamed Ali Jendoubi is Professor at the Université de Carthage, Tunisia. Yomna Rebai is Professor at the Ecole Polytechnique de Tunisie and at the Université de Carthage, Tunisia. Hasna Riahi is Assistant Professor at Ecole Nationale d'Ingénieurs de Tunis, Université Tunis El-Manar, Tunis, Tunisia. Hatem Zaag is a Senior Centre National de la Recherche Scientifique Researcher at Université de Paris XIII, France.
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