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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.
London Mathematical Society Lecture Note Series: Partial Differential Equations Arising from Physics and Geometry: A Volume in Memory of Abbas Bahri Series Number 450
Preface Mohamed Ben Ayed, Mohamed Ali Jendoubi, Yomna Rebai, Hassna Riahi and Hatem Zaag; Abbas Bahri: a dedicated life Mohamed Ben Ayed; 1. Blow-up rate for a semilinear wave equation with exponential nonlinearity in one space dimension Asma Azaiez, Nader Masmoudi and Hatem Zaag; 2. On the role of anisotropy in the weak stability of the Navier-Stokes system Hajer Bahouri, Jean-Yves Chemin and Isabelle Gallagher; 3. The motion law of fronts for scalar reaction-diffusion equations with multiple wells: the degenerate case Fabrice Bethuel and Didier Smets; 4. Finite-time blowup for some nonlinear complex Ginzburg-Landau equations Thierry Cazenave and Seifeddine Snoussi; 5. Asymptotic analysis for the Lane-Emden problem in dimension two Francesca de Marchis, Isabella Ianni and Filomena Pacella; 6. A data assimilation algorithm: the paradigm of the 3D Leray- model of turbulence Aseel Farhat, Evelyn Lunasin and Edriss S. Titi; 7. Critical points at infinity methods in CR geometry Najoua Gamara; 8. Some simple problems for the next generations Alain Haraux; 9. Clustering phenomena for linear perturbation of the Yamabe equation Angela Pistoia and Giusi Vaira; 10. Towards better mathematical models for physics Luc Tartar.