Systems of Conservation Laws 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Systems of Conservation Laws 1 write by Denis Serre. This book was released on 1999-05-27. Systems of Conservation Laws 1 available in PDF, EPUB and Kindle. Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.
Systems of Conservation Laws
Systems of Conservation Laws - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Systems of Conservation Laws write by Yuxi Zheng. This book was released on 2012-12-06. Systems of Conservation Laws available in PDF, EPUB and Kindle. This work should serve as an introductory text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. The only requisite for the reader is a knowledge of the elementary theory of partial differential equations. Key features of this work include: * broad range of topics, from the classical treatment to recent results, dealing with solutions to 2D compressible Euler equations * good review of basic concepts (1-D Riemann problems) * concrete solutions presented, with many examples, over 100 illustrations, open problems, and numerical schemes * numerous exercises, comprehensive bibliography and index * appeal to a wide audience of applied mathematicians, graduate students, physicists, and engineers Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis.
Hyperbolic Systems of Conservation Laws
Hyperbolic Systems of Conservation Laws - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hyperbolic Systems of Conservation Laws write by Alberto Bressan. This book was released on 2000. Hyperbolic Systems of Conservation Laws available in PDF, EPUB and Kindle. This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This volume is the first to present a comprehensive account of these new, fundamental advances. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. A set of problems, with varying difficulty is given at the end of each chapter to verify and expand understanding of the concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference to the state of the art in the field of hyperbolic systems of conservation laws.
Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables write by A. Majda. This book was released on 2012-12-06. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables available in PDF, EPUB and Kindle. Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.
Hyperbolic Systems of Conservation Laws
Hyperbolic Systems of Conservation Laws - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hyperbolic Systems of Conservation Laws write by Philippe G. LeFloch. This book was released on 2012-12-06. Hyperbolic Systems of Conservation Laws available in PDF, EPUB and Kindle. This book examines the well-posedness theory for nonlinear hyperbolic systems of conservation laws, recently completed by the author together with his collaborators. It covers the existence, uniqueness, and continuous dependence of classical entropy solutions. It also introduces the reader to the developing theory of nonclassical (undercompressive) entropy solutions. The systems of partial differential equations under consideration arise in many areas of continuum physics.
