Geometry Of Pdes And Related Problems

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Geometry Of Pdes And Related Problems

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Author : Xavier Cabré
language : en
Publisher: Springer
Release Date : 2018-10-03

Geometry Of Pdes And Related Problems written by Xavier Cabré and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references. Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

Geometry In Partial Differential Equations

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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 1994

Geometry In Partial Differential Equations written by Agostino Prastaro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

Geometric Methods In Inverse Problems And Pde Control

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Author : Chrisopher B. Croke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Geometric Methods In Inverse Problems And Pde Control written by Chrisopher B. Croke 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.

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.

Partial Differential Equations Arising From Physics And Geometry

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Author : Mohamed Ben Ayed
language : en
Publisher: Cambridge University Press
Release Date : 2019-04-30

Partial Differential Equations Arising From Physics And Geometry written by Mohamed Ben Ayed and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-30 with Mathematics categories.

In this edited volume leaders in the field of partial differential equations present recent work on topics in PDEs arising from geometry and physics. The papers originate from a 2015 research school organized by CIMPA and MIMS in Hammamet, Tunisia to celebrate the 60th birthday of the late Professor Abbas Bahri. The opening chapter commemorates his life and work. While the research presented in this book is cutting-edge, the treatment throughout is at a level accessible to graduate students. It includes short courses offering readers a unique opportunity to learn the state of the art in evolution equations and mathematical models in physics, which will serve as an introduction for students and a useful reference for established researchers. Finally, the volume includes many open problems to inspire the next generation.

Lectures On Partial Differential Equations

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Author : Vladimir I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Lectures On Partial Differential Equations written by Vladimir I. Arnold 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 2013-06-29 with Mathematics categories.

Choice Outstanding Title! (January 2006) Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries equation are also discussed. Physical intuition is emphasized. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.

Lecture Notes On Geometrical Aspects Of Partial Differential Equations

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Author : Viktor Viktorovich Zharinov
language : en
Publisher: World Scientific
Release Date : 1992

Lecture Notes On Geometrical Aspects Of Partial Differential Equations written by Viktor Viktorovich Zharinov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This book focuses on the properties of nonlinear systems of PDE with geometrical origin and the natural description in the language of infinite-dimensional differential geometry. The treatment is very informal and the theory is illustrated by various examples from mathematical physics. All necessary information about the infinite-dimensional geometry is given in the text.

Partial Differential Equations For Geometric Design

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Author : Hassan Ugail
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-24

Partial Differential Equations For Geometric Design written by Hassan Ugail 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 2011-08-24 with Computers categories.

The subject of Partial Differential Equations (PDEs) which first emerged in the 18th century holds an exciting and special position in the applications relating to the mathematical modelling of physical phenomena. The subject of PDEs has been developed by major names in Applied Mathematics such as Euler, Legendre, Laplace and Fourier and has applications to each and every physical phenomenon known to us e.g. fluid flow, elasticity, electricity and magnetism, weather forecasting and financial modelling. This book introduces the recent developments of PDEs in the field of Geometric Design particularly for computer based design and analysis involving the geometry of physical objects. Starting from the basic theory through to the discussion of practical applications the book describes how PDEs can be used in the area of Computer Aided Design and Simulation Based Design. Extensive examples with real life applications of PDEs in the area of Geometric Design are discussed in the book.

Some Nonlinear Problems In Riemannian Geometry

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Author : Thierry Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Some Nonlinear Problems In Riemannian Geometry written by Thierry Aubin 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 2013-03-09 with Mathematics categories.

During the last few years, the field of nonlinear problems has undergone great development. This book consisting of the updated Grundlehren volume 252 by the author and of a newly written part, deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus, the reader is given access, for each specific problem, to its present status of solution as well as to the most up-to-date methods for approaching it. The main objective of the book is to explain some methods and new techniques, and to apply them. It deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber.

Differential Geometry Differential Equations And Mathematical Physics

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Author : Maria Ulan
language : en
Publisher: Springer Nature
Release Date : 2021-02-12

Differential Geometry Differential Equations And Mathematical Physics written by Maria Ulan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-12 with Mathematics categories.

This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.

Differential Geometry And Analysis On Cr Manifolds

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Author : Sorin Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-10

Differential Geometry And Analysis On Cr Manifolds written by Sorin Dragomir 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 2007-06-10 with Mathematics categories.

Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study