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Some Qualitative Properties Of 2x2 Systems Of Conservation Laws Of Mixed Type
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Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher : ISBN 13 : Total Pages :12 pages Book Rating :4.:/5 (123 download)
Book Synopsis Some Qualitative Properties of 2x2 Systems of Conservation Laws of Mixed Type by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Some Qualitative Properties of 2x2 Systems of Conservation Laws of Mixed Type written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1989 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some qualitative properties of 2 X 2 systems of conservation laws of mixed type by : Helge Holden
Download or read book Some qualitative properties of 2 X 2 systems of conservation laws of mixed type written by Helge Holden and published by . This book was released on 1988 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling and Analysis of Diffusive and Advective Processes in Geosciences by : William Edward Fitzgibbon
Download or read book Modeling and Analysis of Diffusive and Advective Processes in Geosciences written by William Edward Fitzgibbon and published by SIAM. This book was released on 1992-01-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Not a collection of proceedings, but 11 papers on topics that emerged from a September 1989 conference in Houston on mathematical and computational issues in geophysical fluid and solid mechanics. The discussions include a semi-linear heat equation subject to the specification of energy, an analytic
Book Synopsis Well-Posedness for General 2X2 Systems of Conservation Laws by : Andrea Marson
Download or read book Well-Posedness for General 2X2 Systems of Conservation Laws written by Andrea Marson and published by American Mathematical Soc.. This book was released on 2004-03-19 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the Cauchy problem for a strictly hyperbolic $2\times 2$ system of conservation laws in one space dimension $u_t+[F(u)]_x=0, u(0,x)=\bar u(x),$ which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic fields. If $r_i(u), \ i=1,2,$ denotes the $i$-th right eigenvector of $DF(u)$ and $\lambda_i(u)$ the corresponding eigenvalue, then the set $\{u : \nabla \lambda_i \cdot r_i (u) = 0\}$ is a smooth curve in the $u$-plane that is transversal to the vector field $r_i(u)$. Systems of conservation laws that fulfill such assumptions arise in studying elastodynamics or rigid heat conductors at low temperature. For such systems we prove the existence of a closed domain $\mathcal{D} \subset L^1,$ containing all functions with sufficiently small total variation, and of a uniformly Lipschitz continuous semigroup $S:\mathcal{D} \times [0,+\infty)\rightarrow \mathcal{D}$ with the following properties. Each trajectory $t \mapsto S_t \bar u$ of $S$ is a weak solution of (1). Vice versa, if a piecewise Lipschitz, entropic solution $u= u(t,x)$ of (1) exists for $t \in [0,T],$ then it coincides with the trajectory of $S$, i.e. $u(t,\cdot) = S_t \bar u.$ This result yields the uniqueness and continuous dependence of weak, entropy-admissible solutions of the Cauchy problem (1) with small initial data, for systems satisfying the above assumption.
Book Synopsis Numerical Methods for Conservation Laws by : LEVEQUE
Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Physics Briefs written by and published by . This book was released on 1987 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Hybrid Dynamical Systems by : Arjan J. van der Schaft
Download or read book An Introduction to Hybrid Dynamical Systems written by Arjan J. van der Schaft and published by Springer. This book was released on 2007-10-03 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of the interaction between discrete and continuous dynamics. The present volume provides a first attempt in book form to bring together concepts and methods dealing with hybrid systems from various areas, and to look at these from a unified perspective. The authors have chosen a mode of exposition that is largely based on illustrative examples rather than on the abstract theorem-proof format because the systematic study of hybrid systems is still in its infancy. The examples are taken from many different application areas, ranging from power converters to communication protocols and from chaos to mathematical finance. Subjects covered include the following: definition of hybrid systems; description formats; existence and uniqueness of solutions; special subclasses (variable-structure systems, complementarity systems); reachability and verification; stability and stabilizability; control design methods. The book will be of interest to scientists from a wide range of disciplines including: computer science, control theory, dynamical system theory, systems modeling and simulation, and operations research.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Hyperbolic Systems of Conservation Laws by : Alberto Bressan
Download or read book Hyperbolic Systems of Conservation Laws written by Alberto Bressan and published by Oxford University Press, USA. This book was released on 2000 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Partial Differential Equations by : Peter J. Olver
Download or read book Introduction to Partial Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.
Book Synopsis An Introduction to Mathematical Modeling by : Edward A. Bender
Download or read book An Introduction to Mathematical Modeling written by Edward A. Bender and published by Courier Corporation. This book was released on 2012-05-23 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
Book Synopsis Shock Waves and Reaction—Diffusion Equations by : Joel Smoller
Download or read book Shock Waves and Reaction—Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.
Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Book Synopsis Scaling of Differential Equations by : Hans Petter Langtangen
Download or read book Scaling of Differential Equations written by Hans Petter Langtangen and published by Springer. This book was released on 2016-06-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Book Synopsis Properties of Materials by : Robert E. Newnham
Download or read book Properties of Materials written by Robert E. Newnham and published by Oxford University Press on Demand. This book was released on 2005 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, matrices, symmetry, and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anistropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to qualify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and party on the basic physics and chemistry of materials.
Book Synopsis Computational Thermodynamics of Materials by : Zi-Kui Liu
Download or read book Computational Thermodynamics of Materials written by Zi-Kui Liu and published by Cambridge University Press. This book was released on 2016-06-30 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates fundamental concepts with experimental data and practical applications, including worked examples and end-of-chapter problems.
Book Synopsis Fundamentals of Numerical Reservoir Simulation by : D.W. Peaceman
Download or read book Fundamentals of Numerical Reservoir Simulation written by D.W. Peaceman and published by Elsevier. This book was released on 2000-04-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of numerical reservoir simulation with high-speed electronic computers has gained wide acceptance throughout the petroleum industry for making engineering studies of a wide variety of oil and gas reservoirs throughout the world. These reservoir simulators have been designed for use by reservoir engineers who possess little or no background in the numerical mathematics upon which they are based. In spite of the efforts to improve numerical methods to make reservoir simulators as reliable, efficient, and automatic as possible, the user of a simulator is faced with a myriad of decisions that have nothing to do with the problem to be solved. This book combines a review of some basic reservoir mechanics with the derivation of the differential equations that reservoir simulators are designed to solve.
