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Well Posedness Of The Cauchy Problem For N Xn Systems Of Conservation Laws
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Book Synopsis Well-Posedness of the Cauchy Problem for n Xn Systems of Conservation Laws by : Alberto Bressan
Download or read book Well-Posedness of the Cauchy Problem for n Xn Systems of Conservation Laws written by Alberto Bressan and published by American Mathematical Soc.. This book was released on 2000 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and researchers interested in the mathematical physics and PDE.
Book Synopsis Well-Posedness of the Cauchy Problem for N Times N Systems of Conservation by : Alberto Bressan
Download or read book Well-Posedness of the Cauchy Problem for N Times N Systems of Conservation written by Alberto Bressan and published by . This book was released on 2014-09-11 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and researchers interested in the mathematical physics and PDE.
Book Synopsis Well-posedness for General 2 X 2 Systems of Conservation Laws by : Fabio Ancona
Download or read book Well-posedness for General 2 X 2 Systems of Conservation Laws written by Fabio Ancona and published by American Mathematical Soc.. This book was released on 2004 with total page 170 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). Viceversa, 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 with small initial data, for systems satysfying the above assumption.
Book Synopsis Nonlinear Conservation Laws and Applications by : Alberto Bressan
Download or read book Nonlinear Conservation Laws and Applications written by Alberto Bressan and published by Springer Science & Business Media. This book was released on 2011-04-19 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.
Book Synopsis Distribution Solutions of Nonlinear Systems of Conservation Laws by : Michael Sever
Download or read book Distribution Solutions of Nonlinear Systems of Conservation Laws written by Michael Sever and published by American Mathematical Soc.. This book was released on 2007 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The local structure of solutions of initial value problems for nonlinear systems of conservation laws is considered. Given large initial data, there exist systems with reasonable structural properties for which standard entropy weak solutions cannot be continued after finite time, but for which weaker solutions, valued as measures at a given time, exist. At any given time, the singularities thus arising admit representation as weak limits of suitable approximate solutions in the space of measures with respect to the space variable. Two distinct classes of singularities have emerged in this context, known as delta-shocks and singular shocks. Notwithstanding the similar form of the singularities, the analysis of delta-shocks is very different from that of singular shocks, as are the systems for which they occur. Roughly speaking, the difference is that for delta-shocks, the density approximations majorize the flux approximations, whereas for singular shocks, the flux approximations blow up faster. As against that admissible singular shocks have viscous structure.
Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications by : Heinrich Freistühler
Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Heinrich Freistühler and published by Birkhäuser. This book was released on 2013-12-01 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Eighth International Conference on Hyperbolic Problems - Theory, Nu merics, Applications, was held in Magdeburg, Germany, from February 27 to March 3, 2000. It was attended by over 220 participants from many European countries as well as Brazil, Canada, China, Georgia, India, Israel, Japan, Taiwan, und the USA. There were 12 plenary lectures, 22 further invited talks, and around 150 con tributed talks in parallel sessions as well as posters. The speakers in the parallel sessions were invited to provide a poster in order to enhance the dissemination of information. Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. Despite considerable progress, the mathematical theory is still strug gling with fundamental open problems concerning systems of such equations in multiple space dimensions. For various applications the development of accurate and efficient numerical schemes for computation is of fundamental importance. Applications touched in these proceedings concern one-phase and multiphase fluid flow, phase transitions, shallow water dynamics, elasticity, extended ther modynamics, electromagnetism, classical and relativistic magnetohydrodynamics, cosmology. Contributions to the abstract theory of hyperbolic systems deal with viscous and relaxation approximations, front tracking and wellposedness, stability ofshock profiles and multi-shock patterns, traveling fronts for transport equations. Numerically oriented articles study finite difference, finite volume, and finite ele ment schemes, adaptive, multiresolution, and artificial dissipation methods.
Book Synopsis Analytical Approaches to Multidimensional Balance Laws by : Olga S. Rozanova
Download or read book Analytical Approaches to Multidimensional Balance Laws written by Olga S. Rozanova and published by Nova Publishers. This book was released on 2006 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is difficult to overestimate the importance of mathematical investigation of balance laws. They arise in many areas of physics, mechanics, chemistry, biology, social sciences. In this collective book we concentrate in particular on the equations of continuous medium and related to them. As a rule, they are very complicated in their primitive form. An important feature of such equations is a possible formation of singularities even in initially smooth solution within a finite time. The structure of the singularities can be very complex. A natural step in the approach to this problem is the transition, despite the three-dimensionality of our world, to spatially one-dimensional model. Significant progress has been achieved in this direction. Unfortunately, the methods of the one-dimensional theory, as usual, cannot be adapted to a case of many spatial variables. However, there are many attempts to deal with multidimensional problems. We would like to present some of them. All of the papers are written by outstanding experts, representing various schools in mathematics and mechanics. Each paper is organised as follows: it contains an elementary (as far as it is possible) introduction to a problem, a brief review of previously published results, and then original results of the authors are presented.
Author :Constantine M. Dafermos Publisher :Springer Science & Business Media ISBN 13 :9783540254522 Total Pages :650 pages Book Rating :4.2/5 (545 download)
Book Synopsis Hyperbolic Conservation Laws in Continuum Physics by : Constantine M. Dafermos
Download or read book Hyperbolic Conservation Laws in Continuum Physics written by Constantine M. Dafermos and published by Springer Science & Business Media. This book was released on 2005-08-24 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a lucid and authoritative exposition of the mathematical theory of hyperbolic system laws. The second edition contains a new chapter recounting exciting recent developments on the vanishing viscosity method. Numerous new sections introduce newly derived results. From the reviews: "The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH
Book Synopsis Nonlinear Conservation Laws, Fluid Systems and Related Topics by : Gui-Qiang Chen
Download or read book Nonlinear Conservation Laws, Fluid Systems and Related Topics written by Gui-Qiang Chen and published by World Scientific. This book was released on 2009 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at the 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world''s leading experts in the field. The volume comprises five chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible fluid flows, kinetic theory and conservation laws, to statistical theories for fluid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as each chapter leads readers from the basics to the frontiers of the current research in these areas.
Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications by : Thomas Y. Hou
Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Thomas Y. Hou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on "Hyperbolic Problems: Theory, Numerics and Applications'' was held in CalTech on March 25-30, 2002. The conference was the ninth meeting in the bi-annual international series which became one of the highest quality and most successful conference series in Applied mathematics. This volume contains more than 90 contributions presented in this conference, including plenary presentations by A. Bressan, P. Degond, R. LeVeque, T.-P. Liu, B. Perthame, C.-W. Shu, B. Sjögreen and S. Ukai. Reflecting the objective of series, the contributions in this volume keep the traditional blend of theory, numerics and applications. The Hyp2002 meeting placed a particular emphasize on fundamental theory and numerical analysis, on multi-scale analysis, modeling and simulations, and on geophysical applications and free boundary problems arising from materials science and multi-component fluid dynamics. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.
Book Synopsis Analysis of Systems of Conservation Laws by : Heinrich Freistuhler
Download or read book Analysis of Systems of Conservation Laws written by Heinrich Freistuhler and published by CRC Press. This book was released on 1998-12-30 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of continuum mechanics. This field of nonlinear analysis is currently experiencing a marked increase in successful research activity. The EU-TMR network "Hyperbolic Systems of Conservation Laws held a summer program offering short courses on the Analysis of Systems of Conservation Laws. This book contains five of the self-contained short courses presented during this program by experts of international reputation. These courses, which address solutions to hyperbolic systems by the front tracking method, non-strictly hyperbolic conservation laws, hyperbolic-elliptic coupled systems, hyperbolic relaxation problems, the stability of nonlinear waves in viscous media and numerics, and more, represent the state of the art of most central aspects of the field.
Book Synopsis Hyperbolic Problems: Theory, Numerics and Applications by : Eitan Tadmor
Download or read book Hyperbolic Problems: Theory, Numerics and Applications written by Eitan Tadmor and published by American Mathematical Soc.. This book was released on 2009 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.
Book Synopsis Progress in Analysis by : Heinrich G. W. Begehr
Download or read book Progress in Analysis written by Heinrich G. W. Begehr and published by World Scientific. This book was released on 2003 with total page 1557 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Book Synopsis Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) by : Heinrich G W Begehr
Download or read book Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) written by Heinrich G W Begehr and published by World Scientific. This book was released on 2003-08-04 with total page 1556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Book Synopsis Advances in Differential Equations and Mathematical Physics by : Yulia E. Karpeshina
Download or read book Advances in Differential Equations and Mathematical Physics written by Yulia E. Karpeshina and published by American Mathematical Soc.. This book was released on 2003 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the 9th International Conference on Differential Equations and Mathematical Physics. It contains 29 research and survey papers contributed by conference participants. The conference provided researchers a forum to present and discuss their recent results in a broad range of areas encompassing the theory of differential equations and their applications in mathematical physics. Papers in this volume represent some of the most interesting results and the major areas of research that were covered, including spectral theory with applications to non-relativistic and relativistic quantum mechanics, including time-dependent and random potential, resonances, many body systems, pseudodifferential operators and quantum dynamics, inverse spectral and scattering problems, the theory of linear and nonlinear partial differential equations with applications in fluid dynamics, conservation laws and numerical simulations, as well as equilibrium and nonequilibrium statistical mechanics. The volume is intended for graduate students and researchers interested in mathematical physics.
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 Nonlinear Partial Differential Equations by : Gui-Qiang Chen
Download or read book Nonlinear Partial Differential Equations written by Gui-Qiang Chen and published by American Mathematical Soc.. This book was released on 1999 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of original research papers and expository articles stemming from the scientific program of the Nonlinear PDE Emphasis Year held at Northwestern University (Evanston, IL) in March 1998. The book offers a cross-section of the most significant recent advances and current trends and directions in nonlinear partial differential equations and related topics. The book's contributions offer two perspectives. There are papers on general analytical treatment of the theory and papers on computational methods and applications originating from significant realistic mathematical models of natural phenomena. Also included are articles that bridge the gap between these two perspectives, seeking synergistic links between theory and modeling and computation. The volume offers direct insight into recent trends in PDEs. This volume is also available on the Web. Those who purchase the print edition can gain free access by going to www.ams.org/conm/.
