Evolution Equations and Lagrangian Coordinates

Evolution Equations and Lagrangian Coordinates

Author: Anvarbek M. Meirmanov

Publisher: Walter de Gruyter

Published: 2011-07-20

Total Pages: 329

ISBN-13: 311087444X

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)


Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium

Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium

Author: Tatsien Li

Publisher: World Scientific

Published: 1999-08-31

Total Pages: 334

ISBN-13: 9814543446

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This book discusses recent trends and developments in the area of nonlinear evolution equations. It is a collection of invited lectures on the following topics: nonlinear parabolic equations (systems); nonlinear hyperbolic systems; free boundary problems; conservation laws and shock waves; travelling and solitary waves; regularity, stability and singularity, etc.


Evolution Equations

Evolution Equations

Author: David Ellwood

Publisher: American Mathematical Soc.

Published: 2013-06-26

Total Pages: 587

ISBN-13: 0821868616

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This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).


Nonlinear Evolution Equations and Related Topics

Nonlinear Evolution Equations and Related Topics

Author: Wolfgang Arendt

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 803

ISBN-13: 3034879245

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Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.


Multiscale Thermo-Dynamics

Multiscale Thermo-Dynamics

Author: Michal Pavelka

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-08-06

Total Pages: 363

ISBN-13: 3110387530

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One common feature of new emerging technologies is the fusion of the very small (nano) scale and the large scale engineering. The classical environment provided by single scale theories, as for instance by the classical hydrodynamics, is not anymore satisfactory. The main challenge is to keep the important details while still be able to keep the overall picture and simplicity. It is the thermodynamics that addresses this challenge. Our main reason for writing this book is to explain such general viewpoint of thermodynamics and to illustrate it on a very wide range of examples. Contents Levels of description Hamiltonian mechanics Irreversible evolution Reversible and irreversible evolution Multicomponent systems Contact geometry Appendix: Mathematical aspects


Energy Methods in Continuum Mechanics

Energy Methods in Continuum Mechanics

Author: S.N. Antontsev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 180

ISBN-13: 9400903375

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This volume contains the proceedings of the Workshop Energy Methods for Free Boundary Problems in Continuum Mechanics, held in Oviedo, Spain, from March 21 to March 23, 1994. It is well known that the conservation laws and the constitutive equations of Continuum Mechanics lead to complicated coupled systems of partial differential equations to which, as a rule, one fails to apply the techniques usually employed in the studies of scalar uncoupled equations such as, for instance, the maximum principle. The study of the qualitative behaviour of solutions of the systems re quires different techniques, among others, the so called, Energy Methods where the properties of some integral of a nonnegative function of one or several unknowns allow one to arrive at important conclusions on the envolved unknowns. This vol ume presents the state of the art in such a technique. A special attention is paid to the class of Free Boundary Problems. The organizers are pleased to thank the European Science Foundation (Pro gram on Mathematical treatment of free boundary problems), the DGICYT (Spain), the FICYT (Principado de Asturias, Spain) and the Universities of Oviedo and Complutense de Madrid for their generous financial support. Finally, we wish to thank Kluwer Academic Publishers for the facilities received for the publication of these Proceedings.


Dark Matter in the Universe

Dark Matter in the Universe

Author: Società italiana di fisica

Publisher: IOS Press

Published: 1996

Total Pages: 739

ISBN-13: 1614992177

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Physics and astrophysics came to dark matter through many different routes, finally accepting it, but often with some distaste. It has been noticed that the existence of dark matter is yet another displacement of humans from the centre of the Universe: not only do our planet and our sun have no central position in the Universe, not only are humans just animals (although with a 'specialized' central nervous system), but even the material of which we are made is only a marginal component of the cosmic substance! If this is the right attitude to take, scientists feeling distaste for dark matter are much like Galileo Galilei's colleagues who refused to look through the telescope to watch the Medici planets. Nevertheless, astronomers, when required to take a ballot in favour of some cosmological model, often still vote for 'pure baryonic' with substantial majorities, although most cosmologists assume that a 'cold' component of dark matter plays a role in producing the world as we observe it. Among the many subjects covered by the book, particular emphasis was given to 1) summarizing the current status of the observations both of the distribution of the nearby galaxies and of the evolution of more distant galaxies; 2) advanced statistical techniques for quantifying structure in galaxy redshift and peculiar velocity surveys; 3) the art of cosmic inflation and models for dark matter candidates, and their implications for cosmic microwave background observations; 4) implications of cold dark matter variants for large scale structure, as worked out both by quasi-linear techniques and by fully nonlinear simulations; and 5) Eulerian and Lagrangian approximations for treating the nonlinear dynamics.


Proceedings of the 4th European Conference, Elliptic and Parabolic Problems

Proceedings of the 4th European Conference, Elliptic and Parabolic Problems

Author: Josef Bemelmans

Publisher: World Scientific

Published: 2002

Total Pages: 508

ISBN-13: 9789812380456

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This book provides an overview of the state of the art in important subjects, including ? besides elliptic and parabolic issues ? geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis.


Elliptic and Parabolic Problems

Elliptic and Parabolic Problems

Author: Catherine Bandle

Publisher: Springer Science & Business Media

Published: 2006-01-17

Total Pages: 466

ISBN-13: 3764373849

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Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis, and this volume collects contributions by his former students and collaborators in honor of his 60th anniversary at a conference in Gaeta. It presents new developments in the theory of partial differential equations with emphasis on elliptic and parabolic problems.