Global Propagation Of Regular Nonlinear Hyperbolic Waves
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Global Propagation Of Regular Nonlinear Hyperbolic Waves
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Author : Tatsien Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-01
Global Propagation Of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-01 with Science categories.
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.
Global Propagation Of Regular Nonlinear Hyperbolic Waves
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Author : Tatsien Li
language : en
Publisher: Birkhäuser
Release Date : 2011-11-02
Global Propagation Of Regular Nonlinear Hyperbolic Waves written by Tatsien Li and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-02 with Science categories.
This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically beginning with introductory material and leading to the original research of the authors. Topics are motivated with a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Aimed at researchers and graduate students in partial differential equations and related topics, this book will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves.
Hyperbolic Conservation Laws In Continuum Physics
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Author : Constantine M. Dafermos
language : en
Publisher: Springer
Release Date : 2016-05-26
Hyperbolic Conservation Laws In Continuum Physics written by Constantine M. Dafermos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-26 with Mathematics categories.
OLD TEXT 4th Edition to be replaced: This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles. From the reviews of the 3rd edition: "This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject." Evgeniy Panov, Zentralblatt MATH "A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the "Bible" on the subject." Philippe G. LeFloch, Math. Reviews
Emerging Topics On Differential Equations And Their Applications Proceedings On Sino Japan Conference Of Young Mathematicians
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Author : Yiming Long
language : en
Publisher: World Scientific
Release Date : 2012-12-31
Emerging Topics On Differential Equations And Their Applications Proceedings On Sino Japan Conference Of Young Mathematicians written by Yiming Long and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Mathematics categories.
The aim of the Sino-Japan Conference of Young Mathematicians was to provide a forum for presenting and discussing recent trends and developments in differential equations and their applications, as well as to promote scientific exchanges and collaborations among young mathematicians both from China and Japan.The topics discussed in this proceedings include mean curvature flows, KAM theory, N-body problems, flows on Riemannian manifolds, hyperbolic systems, vortices, water waves, and reaction diffusion systems.
Recent Progress In Computational And Applied Pdes
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Author : Tony F. Chan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Recent Progress In Computational And Applied Pdes written by Tony F. Chan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The book discusses some key scientific and technological developments in computational and applied partial differential equations. It covers many areas of scientific computing, including multigrid methods, image processing, finite element analysis and adaptive computations. It also covers software technology, algorithms and applications. Most papers are of research level, and are contributed by some well-known mathematicians and computer scientists. The book will be useful to engineers, computational scientists and graduate students.
Linear And Quasi Linear Evolution Equations In Hilbert Spaces
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Author : Pascal Cherrier
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-14
Linear And Quasi Linear Evolution Equations In Hilbert Spaces written by Pascal Cherrier and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-14 with Mathematics categories.
This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasi-linear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely self-contained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations.
Input To State Stability For Pdes
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Author : Iasson Karafyllis
language : en
Publisher: Springer
Release Date : 2018-06-07
Input To State Stability For Pdes written by Iasson Karafyllis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Technology & Engineering categories.
This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.
Energy Transfers In Atmosphere And Ocean
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Author : Carsten Eden
language : en
Publisher: Springer
Release Date : 2019-01-23
Energy Transfers In Atmosphere And Ocean written by Carsten Eden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-23 with Mathematics categories.
This book describes a recent effort combining interdisciplinary expertise within the Collaborative Research Centre “Energy transfers in atmosphere and ocean” (TRR-181), which was funded by the German Research Foundation (DFG). Energy transfers between the three dynamical regimes – small-scale turbulence, internal gravity waves and geostrophically balanced motion – are fundamental to the energy cycle of both the atmosphere and the ocean. Nonetheless, they remain poorly understood and quantified, and have yet to be adequately represented in today’s climate models. Since interactions between the dynamical regimes ultimately link the smallest scales to the largest ones through a range of complex processes, understanding these interactions is essential to constructing atmosphere and ocean models and to predicting the future climate. To this end, TRR 181 combines expertise in applied mathematics, meteorology, and physical oceanography. This book provides an overview of representative specific topics addressed by TRR 181, ranging from - a review of a coherent hierarchy of models using consistent scaling and approximations, and revealing the underlying Hamiltonian structure - a systematic derivation and implementation of stochastic and backscatter parameterisations - an exploration of the dissipation of large-scale mean or eddying balanced flow and ocean eddy parameterisations; and - a study on gravity wave breaking and mixing, the interaction of waves with the mean flow and stratification, wave-wave interactions and gravity wave parameterisations to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface. In TRR 181, the process-oriented topics presented here are complemented by an operationally oriented synthesis focusing on two climate models currently being developed in Germany. In this way, the goal of TRR 181 is to help reduce the biases in and increase the accuracy of atmosphere and ocean models, and ultimately to improve climate models and climate predictions.
Coastal Engineering 2008 In 5 Volumes Proceedings Of The 31st International Conference
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Author : Jane Mckee Smith
language : en
Publisher: World Scientific
Release Date : 2009-05-05
Coastal Engineering 2008 In 5 Volumes Proceedings Of The 31st International Conference written by Jane Mckee Smith and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-05 with Technology & Engineering categories.
This proceedings contains papers presented at the 31st International Conference on Coastal Engineering, which has held in Hamburg, Germany (31 August - 5 September 2008). The proceeding is divided into five parts: Waves; Long Waves, Nearshore Currents, and Swash; Sediment Transport and Morphology; Coastal Management, Environment, and Risk; and Coastal Structures. The papers cover a broad range of topics including theory, numerical and physical modeling, field measurements, case studies, design, and management. Coastal Engineering 2008 provides coastal engineers, scientists, and planners, with state-of-the-art information on coastal engineering and coastal processes.
Progress In Partial Differential Equations
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Author : Michael Reissig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-30
Progress In Partial Differential Equations written by Michael Reissig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-30 with Mathematics categories.
Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society. This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The readers will find this an excellent resource of both introductory and advanced material. The key topics are: • Linear hyperbolic equations and systems (scattering, symmetrisers) • Non-linear wave models (global existence, decay estimates, blow-up) • Evolution equations (control theory, well-posedness, smoothing) • Elliptic equations (uniqueness, non-uniqueness, positive solutions) • Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)