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Product Code:  AMSIP/15 
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eBook ISBN:  9781470438067 
Product Code:  AMSIP/15.E 
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Softcover ISBN:  9780821819654 
eBook: ISBN:  9781470438067 
Product Code:  AMSIP/15.B 
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MAA Member Price:  $100.80 $76.50 
AMS Member Price:  $89.60 $68.00 
Softcover ISBN:  9780821819654 
Product Code:  AMSIP/15 
List Price:  $58.00 
MAA Member Price:  $52.20 
AMS Member Price:  $46.40 
eBook ISBN:  9781470438067 
Product Code:  AMSIP/15.E 
List Price:  $54.00 
MAA Member Price:  $48.60 
AMS Member Price:  $43.20 
Softcover ISBN:  9780821819654 
eBook ISBN:  9781470438067 
Product Code:  AMSIP/15.B 
List Price:  $112.00 $85.00 
MAA Member Price:  $100.80 $76.50 
AMS Member Price:  $89.60 $68.00 

Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 15; 2000; 226 ppMSC: Primary 35; Secondary 76; 46;
This volume resulted from a yearlong 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. 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 \(L^1\)wellposedness 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 semiconductor 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This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the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.ReadershipResearchers, graduate students, physicists and engineers who are interested in nonlinear partial differential equations, nonlinear analysis, conservation laws, shocks and singularities, and related topics.

Table of Contents

Chapters

Stability of entropy solutions to n x n conservation laws

Compactness methods and nonlinear hyperbolic conservation laws

Mathematical modelling of microelectronics semiconductor devices

Lecture notes on kinetic formulation of conservation laws

Theory of viscous conservation laws

Some problems of incompressible fluid dynamics


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This volume resulted from a yearlong 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. 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 \(L^1\)wellposedness 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 semiconductor 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.
Researchers, graduate students, physicists and engineers who are interested in nonlinear partial differential equations, nonlinear analysis, conservation laws, shocks and singularities, and related topics.

Chapters

Stability of entropy solutions to n x n conservation laws

Compactness methods and nonlinear hyperbolic conservation laws

Mathematical modelling of microelectronics semiconductor devices

Lecture notes on kinetic formulation of conservation laws

Theory of viscous conservation laws

Some problems of incompressible fluid dynamics