Nonlinear Conservation Laws Fluid Systems And Related Topics

Author : Gui-Qiang Chen
Publisher : World Scientific
Page : 401 pages
File Size : 54,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9789814273275

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Nonlinear Conservation Laws, Fluid Systems and Related Topics by Gui-Qiang Chen Pdf

This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world's leading experts in the field. The volume comprises ªve chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible ªuid ªows, kinetic theory and conservation laws, to statistical theories for ªuid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as each chapter leads readers from the basics to the frontiers of the current research in these areas.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,8 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9789814467940

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Nonlinear Conservation Laws, Fluid Systems and Related Topics by Anonim Pdf

Author : Ling Hsiao,Zhouping Xin,Morningside Center of Mathematics
Publisher : American Mathematical Soc.
Page : 260 pages
File Size : 54,6 Mb
Release : 2000
Category : Conservation laws (Mathematics).
ISBN : 9780821819654

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Some Current Topics on Nonlinear Conservation Laws by Ling Hsiao,Zhouping Xin,Morningside Center of Mathematics Pdf

This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Zhouping Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of $-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in the last decade; and the volume concludes with Y. Zheng's lecture on incompressible fluid dynamics. This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis. Titles in this series are co-published with International Press, Cambridge, MA.

Author : Takaaki Nishida
Publisher : Unknown
Page : 266 pages
File Size : 52,8 Mb
Release : 1978
Category : Differential equations, Hyperbolic
ISBN : UOM:39015017341960

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Nonlinear Hyperbolic Equations and Related Topics in Fluid Dynamics by Takaaki Nishida Pdf

Author : Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 49,5 Mb
Release : 2011-04-19
Category : Mathematics
ISBN : 9781441995544

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Nonlinear Conservation Laws and Applications by Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang Pdf

This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.

Author : Tatsien Li,Yuejun Peng,Bopeng Rao
Publisher : World Scientific
Page : 464 pages
File Size : 52,8 Mb
Release : 2010-09-21
Category : Mathematics
ISBN : 9789814464048

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Some Problems On Nonlinear Hyperbolic Equations And Applications by Tatsien Li,Yuejun Peng,Bopeng Rao Pdf

This 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. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Author : Jean-michel Coron,Tatsien Li,Yachun Li
Publisher : World Scientific
Page : 395 pages
File Size : 55,9 Mb
Release : 2019-01-08
Category : Mathematics
ISBN : 9789813276192

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One-dimensional Hyperbolic Conservation Laws And Their Applications by Jean-michel Coron,Tatsien Li,Yachun Li Pdf

This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.

Author : Thomas H. Otway
Publisher : Springer
Page : 128 pages
File Size : 50,5 Mb
Release : 2015-07-08
Category : Mathematics
ISBN : 9783319197616

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Elliptic–Hyperbolic Partial Differential Equations by Thomas H. Otway Pdf

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

Author : Heinrich Freistuhler
Publisher : CRC Press
Page : 276 pages
File Size : 54,6 Mb
Release : 1998-12-30
Category : Mathematics
ISBN : 0849306442

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Analysis of Systems of Conservation Laws by Heinrich Freistuhler Pdf

Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity. The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.

Author : Bao Gang,Coron Jean-michel,Li Ta-tsien
Publisher : World Scientific
Page : 264 pages
File Size : 44,7 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9789813276161

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Control And Inverse Problems For Partial Differential Equations by Bao Gang,Coron Jean-michel,Li Ta-tsien Pdf

This book is a collection of lecture notes for the LIASFMA Hangzhou Autumn School on 'Control and Inverse Problems for Partial Differential Equations' which was held during October 17-22, 2016 at Zhejiang University, Hangzhou, China. This autumn school is one of the activities organized by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA). Established jointly by eight institutions in China and France in 2014, LIASFMA aims at providing a platform for many leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in broad areas of applied mathematics.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in control and inverse problems. And the readers are exposed not only to the basic theories and methods but also to the forefront of research directions in both fields.

Author : Song Jiang,Tatsien Li,Daqian Li
Publisher : World Scientific
Page : 793 pages
File Size : 51,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814417099

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Hyperbolic Problems by Song Jiang,Tatsien Li,Daqian Li Pdf

This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of OC Hyperbolic Partial Differential EquationsOCO. It is aimed at mathematicians, researchers in applied sciences and graduate students."

Author : Coron Jean-michel,Li Tatsien,Wang Wei-min
Publisher : World Scientific
Page : 220 pages
File Size : 54,7 Mb
Release : 2019-08-19
Category : Science
ISBN : 9789811208386

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Harmonic Analysis And Wave Equations by Coron Jean-michel,Li Tatsien,Wang Wei-min Pdf

This book is a collection of lecture notes for the LIASFMA School and Workshop on 'Harmonic Analysis and Wave Equations' which was held on May 8-18, 2017 at Fudan University, in Shanghai, China. The aim of the LIASFMA School and Workshop is to bring together Chinese and French experts to discuss and dissect recent progress in these related fields; and to disseminate state of art, new knowledge and new concepts, to graduate students and junior researchers.The book provides the readers with a unique and valuable opportunity to learn from and communicate with leading experts in nonlinear wave-type equations. The readers will witness the major development with the introduction of modern harmonic analysis and related techniques.

Author : Jean-michel Coron,Tatsien Li,Zhiqiang Wang
Publisher : World Scientific
Page : 315 pages
File Size : 55,6 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9789811271649

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Control Of Partial Differential Equations by Jean-michel Coron,Tatsien Li,Zhiqiang Wang Pdf

This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.

Author : Zhaojun Bai,Weiguo Gao,Yangfeng Su
Publisher : World Scientific
Page : 148 pages
File Size : 53,9 Mb
Release : 2015-09-04
Category : Mathematics
ISBN : 9789814675789

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Matrix Functions and Matrix Equations by Zhaojun Bai,Weiguo Gao,Yangfeng Su Pdf

Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects. Contents:Matrix Functions: A Short Course (Nicholas J Higham and Lijing Lin)A Short Course on Exponential Integrators (Marlis Hochbruck)Matrix Equations and Model Reduction (Peter Benner, Tobias Breiten and Lihong Feng)Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems (Ren-Cang Li)Factorization-Based Sparse Solvers and Preconditioners (Xiaoye Sherry Li) Readership: Researchers and graduate students in numerical and computational mathematics. Key Features:The book covers underlying theory and a variety of algorithms for matrix functions and matrix equations. The book also covers high performance linear system solvers and eigenvalue computations which are computational kernels to matrix functions and matrix equationsThe book provides the current developments and applications beyond the material found in regular university courses and textbooks. It includes a comprehensive list of latest referencesThe authors of the chapters are leading experts who are also well-known for their expository skillsKeywords:Matrix Functions;Matrix Equations;Numerical Linear Algebra;Exponential Integral

Author : Xiao Qing Jin,Seak-Weng Vong
Publisher : World Scientific Publishing Company
Page : 144 pages
File Size : 48,5 Mb
Release : 2016-05-30
Category : Mathematics
ISBN : 9789814749480

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An Introduction to Applied Matrix Analysis by Xiao Qing Jin,Seak-Weng Vong Pdf

It is well known that most problems in science and engineering eventually progress into matrix problems. This book gives an elementary introduction to applied matrix theory and it also includes some new results obtained in recent years. The book consists of eight chapters. It includes perturbation and error analysis; the conjugate gradient method for solving linear systems; preconditioning techniques; and least squares algorithms based on orthogonal transformations, etc. The last two chapters include some latest development in the area. In Chap. 7, we construct optimal preconditioners for functions of matrices. More precisely, let f be a function of matrices. Given a matrix A, there are two choices of constructing optimal preconditioners for f(A). Properties of these preconditioners are studied for different functions. In Chap. 8, we study the Bottcher–Wenzel conjecture and discuss related problems. This is a textbook for senior undergraduate or junior graduate students majoring in science and engineering. The material is accessible to students who, in various disciplines, have basic linear algebra, calculus, numerical analysis, and computing knowledge. The book is also useful to researchers in computational science who are interested in applied matrix theory.