非線性雙曲型方程的一些問題與應(yīng)用

前言

　　This book is a collection of manuscripts from lectures given in the French-Chinese Summer Institute on Applied Mathematics, which was held at the School of Mathematical Sciences of Fudan University from September I to September 21, 2008. This Institute was mainly sponsored by the Centre National de Recherche Scientifique (CNRS) and the National Natural Science Foundation of China (NSFC). The activities were organized by the Institut Sino-Frangais de Mathematiques Appliquees (ISFMA). There were more than 70 participants, including graduate students, postdoctors and junior faculty members from universities and research institutions in China and France. This volume is entitled Some Problems on Nonlinear Hyperbolic Equations and Applications. The volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications, which represent two subjects of the Institute.These topics are important not only for industrial applications but also for the theory of partial differential equations itself. The main propose of the Institute was to present recent progress and results obtained in the domains related to both subjects and to organize discussions for studying important problems by sustainable collaborations. We hope that this experience will be useful for the activities of the French-Chinese collaboration in the future. During the activities of the Institute, more than 30 lectures of 50 minutes each were delivered. The speakers gave their presentation without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. Each lecture was followed by a free discussion of 30 minutes, so that the participants were able to clarify the situation of each problem and to find interesting subjects to be cooperated in the future. Three mini-courses of 3 x 1.5 hours each were given by Jean-Michel Coron (Universite Paris 6, France), Vilmos Komornik (Universite Louis Pasteur de Strasbourg, France) on the control theory and by Thierry Goudon (INRIA Lille-Nord Europe, France) on the mathematical theory for plasmas.The mini-course notes were prepared for all the students before the activities of the Institute. Moreover, in the middle and before the end of the Institute, we organized two sessions of general discussion on the open problems for future investigations by collaboration. The editors would like to express their sincere thanks to all the authors in this volume for their contributions and to all the participants in the Summer Institute. Liqiang Lu, Zhiqiang Wang and Chunlian Zhou deserve our special thanks for their prompt and effective assistance to make the Institute run smoothly. The editors are grateful to the Centre National de Recherche Scientifique (CNRS), the Consulate General of France in Shanghai, the French Embassy in Beijing, the Institut SinoFrangais de Mathematiques Appliqnees (ISFMA), the National Natural Science Foundation of China (NSFC) and the School of Mathematical Sciences of Fudan University for their help and support. Finally, the editors wish to thank Tianfu Zhao (Senior Editor, Higher Education Press) and Chunlian Zhou for their patience and professional assistance.

內(nèi)容概要

本書是現(xiàn)代應(yīng)用數(shù)學(xué)叢書中的一本，主要對非線性雙曲型方程的一些問題與應(yīng)用知識作了介紹。全書分為兩部分：強(qiáng)非線性等離子體模型中的數(shù)學(xué)與數(shù)值分析(Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models)，擬線性雙曲線系統(tǒng)的精確可控性和可觀察性及其應(yīng)用(Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications)。該書可供各大專院校作為教材使用，也可供從事相關(guān)工作的人員作為參考用書使用。

書籍目錄

Part Ⅰ   Mathematical and Numerical Analyses of Strongly Nonlinear Plasma Models  Open Boundary Conditions and Computational Schemes for Schr5dinger Equations with General Potentials and Nonlinearities  On Hydrodynamic Models for LEO Spacecraft Charging  Asymptotic Regimes for Plasma Physics with Strong Magnetic Fields  The Zero-Electron-Mass Limit in the Hydrodynamic Model (Euler-Poisson System)  Modeling and Simulation of Fluid-Particles Flows  Well-Posedness and Stability of Quantum Hydrodynamics for Semiconductors in Ra  Bloch Decomposition-Based Method for High Frequency Waves in Periodic Media  Some Results of the Euler-Poisson System for Plasmas and Semiconductors  Behavior of Discontinuities in Thermoelasticity with Second Sound  The Convergence of Euler-Poisson System to the Incompressible Euler Equations  On the Relaxation-time Limits in Bipolar Hydrodynamic Models for SemiconductorsPart Ⅱ  Exact Controllability and Observability for  Quasilinear Hyperbolic Systems and Applications  Observability in Arbitrary Small Time for Discrete Approximations of Conservative Systems  Logarithmic Decay of Hyperbolic Equations with Arbitrary Small  Boundary Damping  A Remark on the Controllability of a System of Conservation Laws in the Context of Entropy Solutions  Introduction to the Control of PDE's  Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems: Known Results and Open Problems  Waves, Damped Wave and Observation  Control Problems for Fluid Equations  Global Existence of a Degenerate Kirchhoff System with Boundary Dissipation  Remarks on the Controllability of Some Quasilinear Equations

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