AMS/IP Studies in Advanced Mathematics 2000; 226 pp; softcover Volume: 15 ISBN10: 0821819658 ISBN13: 9780821819654 List Price: US$48 Member Price: US$38.40 Order Code: AMSIP/15
 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 wavea 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 This collection of lectures represents previously unpublished expository and research results of experts in nonlinear conservation laws and is an excellent reference for researchers and advanced graduate students in the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 copublished with International Press, Cambridge, MA. Readership Researchers, 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  A. Bressan  Stability of entropy solutions to n x n conservation laws
 G.Q. Chen  Compactness methods and nonlinear hyperbolic conservation laws
 P. Degond  Mathematical modelling of microelectronics semiconductor devices
 B. Perthame  Lecture notes on kinetic formulation of conservation laws
 Z. Xin  Theory of viscous conservation laws
 Y. Zheng  Some problems of incompressible fluid dynamics
