Transport Equations And Multi D Hyperbolic Conservation Laws

Author : Luigi Ambrosio,Gianluca Crippa,Camillo De Lellis,Felix Otto,Michael Westdickenberg
Publisher : Springer Science & Business Media
Page : 141 pages
File Size : 53,8 Mb
Release : 2008-02-17
Category : Mathematics
ISBN : 9783540767817

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Transport Equations and Multi-D Hyperbolic Conservation Laws by Luigi Ambrosio,Gianluca Crippa,Camillo De Lellis,Felix Otto,Michael Westdickenberg Pdf

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. The captivating volume contains surveys of recent deep results and provides an overview of further developments and related open problems. Readers should have basic knowledge of PDE and measure theory.

Author : Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 51,8 Mb
Release : 2011-04-19
Category : Mathematics
ISBN : 9781441995544

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Nonlinear Conservation Laws and Applications by Alberto Bressan,Gui-Qiang G. Chen,Marta Lewicka,Dehua Wang Pdf

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.

Author : Eitan Tadmor,Jian-Guo Liu,Athanasios E. Tzavaras
Publisher : American Mathematical Soc.
Page : 690 pages
File Size : 52,5 Mb
Release : 2009-12-15
Category : Mathematics
ISBN : 9780821847305

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Hyperbolic Problems: Contributed talks by Eitan Tadmor,Jian-Guo Liu,Athanasios E. Tzavaras Pdf

The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, ``HYP2008'', was held at the University of Maryland from June 9-13, 2008. This was the twelfth meeting in the bi-annual international series of HYP conferences which originated in 1986 at Saint-Etienne, France, and over the last twenty years has become one of the highest quality and most successful conference series in Applied Mathematics. This book, the second in a two-part volume, contains more than sixty articles based on contributed talks given at the conference. The articles are written by leading researchers as well as promising young scientists and cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ``hyperbolic PDEs''. This volume will bring readers to the forefront of research in this most active and important area in applied mathematics.

Author : Alberto Bressan,Gui-Quiang G. Chen,Marta Lewicka,Dehua Wang
Publisher : Springer
Page : 491 pages
File Size : 55,8 Mb
Release : 2011-04-26
Category : Mathematics
ISBN : 1441995552

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Nonlinear Conservation Laws and Applications by Alberto Bressan,Gui-Quiang G. Chen,Marta Lewicka,Dehua Wang Pdf

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.

Author : C.M. Dafermos,Eduard Feireisl
Publisher : Elsevier
Page : 653 pages
File Size : 53,6 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9780080465654

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Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf

The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's. Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discusses the most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionary partial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell's capability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other. The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function. The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class of non-linear equations is investigated, with applications to stochastic control and differential games. The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models. - Volume 1 focuses on the abstract theory of evolution - Volume 2 considers more concrete probelms relating to specific applications - Volume 3 reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear PDEs

Author : Phoolan Prasad
Publisher : Springer
Page : 159 pages
File Size : 44,7 Mb
Release : 2018-03-06
Category : Mathematics
ISBN : 9789811075810

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Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws by Phoolan Prasad Pdf

This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved shock front and formation, propagation and interaction of kink lines on it.

Author : Yuxi Zheng
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201410

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Systems of Conservation Laws by Yuxi Zheng Pdf

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.

Author : Franco Flandoli
Publisher : Springer
Page : 182 pages
File Size : 45,6 Mb
Release : 2011-03-02
Category : Mathematics
ISBN : 9783642182310

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Random Perturbation of PDEs and Fluid Dynamic Models by Franco Flandoli Pdf

The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.

Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 52,6 Mb
Release : 2010-10-01
Category : Mathematics
ISBN : 9780821849767

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Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations Pdf

This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.

Author : Yulia E. Karpeshina,Günter Stolz,Rudi Weikard,Yanni Zeng
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 51,9 Mb
Release : 2003
Category : Differential equations
ISBN : 9780821832967

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Advances in Differential Equations and Mathematical Physics by Yulia E. Karpeshina,Günter Stolz,Rudi Weikard,Yanni Zeng Pdf

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.

Author : Claude Le Bris,Pierre-Louis Lions
Publisher : Walter de Gruyter GmbH & Co KG
Page : 156 pages
File Size : 42,8 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110635508

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Parabolic Equations with Irregular Data and Related Issues by Claude Le Bris,Pierre-Louis Lions Pdf

This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.

Author : E.F. Toro
Publisher : Springer Science & Business Media
Page : 1050 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461506638

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Godunov Methods by E.F. Toro Pdf

This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.

Author : Constantine M. Dafermos
Publisher : Springer Science & Business Media
Page : 710 pages
File Size : 51,9 Mb
Release : 2009-12-12
Category : Mathematics
ISBN : 9783642040481

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Hyperbolic Conservation Laws in Continuum Physics by Constantine M. Dafermos Pdf

The 3rd edition is thoroughly revised, applications are substantially enriched, it includes a new account of the early history of the subject (from 1800 to 1957) and a new chapter recounting the recent solution of open problems of long standing in classical aerodynamics. The bibliography comprises now over fifteen hundred titles. 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

Author : Olga S. Rozanova
Publisher : Nova Publishers
Page : 260 pages
File Size : 44,8 Mb
Release : 2006
Category : Science
ISBN : 1594543070

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Analytical Approaches to Multidimensional Balance Laws by Olga S. Rozanova Pdf

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 : Anonim
Publisher : Unknown
Page : 938 pages
File Size : 45,7 Mb
Release : 1995
Category : Meteorology
ISBN : MINN:31951P00361064R

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Monthly Weather Review by Anonim Pdf