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Hyperbolic Equations and Frequency Interactions

Author: Luis A. Caffarelli

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 480

ISBN-13: 0821805924

The research topic for this IAS/PCMS Summer Session was nonlinear wave phenomena. Mathematicians from the more theoretical areas of PDEs were brought together with those involved in applications. The goal was to share ideas, knowledge, and perspectives. How waves, or "frequencies", interact in nonlinear phenomena has been a central issue in many of the recent developments in pure and applied analysis. It is believed that wavelet theory--with its simultaneous localization in both physical and frequency space and its lacunarity--is and will be a fundamental new tool in the treatment of the phenomena. Included in this volume are write-ups of the "general methods and tools" courses held by Jeff Rauch and Ingrid Daubechies. Rauch's article discusses geometric optics as an asymptotic limit of high-frequency phenomena. He shows how nonlinear effects are reflected in the asymptotic theory. In the article "Harmonic Analysis, Wavelets and Applications" by Daubechies and Gilbert the main structure of the wavelet theory is presented. Also included are articles on the more "specialized" courses that were presented, such as "Nonlinear Schrödinger Equations" by Jean Bourgain and "Waves and Transport" by George Papanicolaou and Leonid Ryzhik. Susan Friedlander provides a written version of her lecture series "Stability and Instability of an Ideal Fluid", given at the Mentoring Program for Women in Mathematics, a preliminary program to the Summer Session. This Summer Session brought together students, fellows, and established mathematicians from all over the globe to share ideas in a vibrant and exciting atmosphere. This book presents the compelling results. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Hyperbolic Equations and Frequency Interactions

Author: Luis A. Caffarelli

Publisher: American Mathematical Soc.

Published:

Total Pages: 488

ISBN-13: 9780821886878

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Hyperbolic Equations and Waves

Author: Marcel Froissart

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 403

ISBN-13: 3642870252

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The success of the 1967 Battelle Rencontres was so much appre ciated by the participants and organizers of this experimental set-up that it was soon decided to go on with the experiment. Mathematicians and physicists had found a very suitable frame to overcome their natural shyness, to get occasionally interested into each others' work, to talk 1968 Rencontres have about it, and eventually to know each other. The been organized with the same idea in mind, and even somewhat enlarged in the following sense: the topic chosen - hyperbolic equations and waves - has proved a cornerstone of physics for more than a century and extends over most fields of contemporary physics. It follows immediately that the wide range of physicists concerned could not be represented by more than a couple of specialists in any single field. Thus, aside from bridging the gap between mathematicians and physicists, the 1968 Recontres provided a rather unique occasion to plug many intra disciplinary gaps among physicists. This made the Rencontres quite unpredictable as to how people would - and could - interact, and created a very stimulating environ ment for an unprecedented intellectual venture. From the outside, it may very well look like a hodge-podge of quite unrelated ideas. But it was much less so at the level of day-to-day discussions and informal gatherings where all slowly acquired a comprehensive synthetic view of the subject.

Numerical Methods for Hyperbolic Equations

Author: Elena Vázquez-Cendón

Publisher: CRC Press

Published: 2012-11-05

Total Pages: 436

ISBN-13: 041562150X

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Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics covered include: • Recent advances in the numerical computation of environmental conservation laws with source terms • Multiphase flow and porous media • Numerical methods in astrophysics • Seismology and geophysics modelling • High order methods for hyperbolic conservation laws • Numerical methods for reactive flows • Finite volume and discontinous Galerkin schemes for stiff source term problems • Methods and models for biomedical problems • Numerical methods for reactive flows The research interest of Eleuterio Toro, born in Chile on 16th July 1946, is reflected in Numerical Methods for Hyperbolic Equations, and focuses on: numerical methods for partial differential equations, with particular emphasis on methods for hyperbolic equations; design and application of new algorithms; hyperbolic partial differential equations as mathematical models of various types of processes; mathematical modelling and simulation of physico/chemical processes that include wave propagation phenomena; modelling of multiphase flows; application of models and methods to real problems. Eleuterio Toro received several honours and distinctions, including the honorary title OBE from Queen Elizabeth II (Buckingham Palace, London 2000); Distinguished Citizen of the City of Carahue (Chile, 2001); Life Fellow, Claire Hall, University of Cambridge (UK, 2003); Fellow of the Indian Society for Shock Wave Research (Bangalore, 2005); Doctor Honoris Causa (Universidad de Santiago de Chile, 2008); William Penney Fellow, University of Cambridge (UK, 2010); Doctor Honoris Causa (Universidad de la Frontera, Chile, 2012). Professor Toro is author of two books, editor of two books and author of more than 260 research works. In the last ten years he has been invited and keynote speaker in more than 100 scientific events. Professor Toro has held many visiting appointments round the world, which include several European countries, Japan, China and USA.

Handbook of Mathematical Fluid Dynamics

Author: S. Friedlander

Publisher: Elsevier

Published: 2004-11-20

Total Pages: 702

ISBN-13: 9780444515568

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The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Arithmetic of L-functions

Author: Cristian Popescu

Publisher: American Mathematical Soc.

Published:

Total Pages: 517

ISBN-13: 0821886983

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Computational Complexity Theory

Author: Steven Rudich

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 407

ISBN-13: 082182872X

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Computational Complexity Theory is the study of how much of a given resource is required to perform the computations that interest us the most. Four decades of fruitful research have produced a rich and subtle theory of the relationship between different resource measures and problems. At the core of the theory are some of the most alluring open problems in mathematics. This book presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on computational complexity. The first week gives a general introduction to the field, including descriptions of the basic mo.

Probability Theory and Applications

Author: Elton P. Hsu

Publisher: American Mathematical Soc.

Published: 1999-01-01

Total Pages: 402

ISBN-13: 9780821886885

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The volume gives a balanced overview of the current status of probability theory. An extensive bibliography for further study and research is included. This unique collection presents several important areas of current research and a valuable survey reflecting the diversity of the field.

Arithmetic Algebraic Geometry

Author: Brian David Conrad

Publisher: American Mathematical Soc.

Published:

Total Pages: 588

ISBN-13: 9780821886915

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The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

Analytic and Algebraic Geometry

Author: Jeffery D. McNeal

Publisher: American Mathematical Soc.

Published: 2010-01-01

Total Pages: 601

ISBN-13: 0821872753

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"Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the 'other side' of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists."--Publisher's description.