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 2002-07-01. 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.
Systems of Conservation Laws 1
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.
Numerical Approximation of Hyperbolic Systems of Conservation Laws
Numerical Approximation of 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 Numerical Approximation of Hyperbolic Systems of Conservation Laws write by Edwige Godlewski. This book was released on 2021-08-28. Numerical Approximation of Hyperbolic Systems of Conservation Laws available in PDF, EPUB and Kindle. This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.
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.
Numerical Methods for Conservation Laws
Numerical Methods for 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 Numerical Methods for Conservation Laws write by LEVEQUE. This book was released on 2013-11-11. Numerical Methods for Conservation Laws available in PDF, EPUB and Kindle. These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
