Geometric Partial Differential Equations Part I

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Geometric Partial Differential Equations Part I

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Author :
language : en
Publisher: Elsevier
Release Date : 2020-01-14

Geometric Partial Differential Equations Part I written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-14 with Mathematics categories.

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. - About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization - Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading - The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Geometric Partial Differential Equations Part 2

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Author : Andrea Bonito
language : en
Publisher: Elsevier
Release Date : 2021-01-26

Geometric Partial Differential Equations Part 2 written by Andrea Bonito and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with Mathematics categories.

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. - About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization - Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading - The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Differential Geometry Partial Differential Equations On Manifolds

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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Differential Geometry Partial Differential Equations On Manifolds written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem

Geometric Partial Differential Equations

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Author : Antonin Chambolle
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-17

Geometric Partial Differential Equations written by Antonin Chambolle 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 2014-01-17 with Mathematics categories.

This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

Quantized Partial Differential Equations

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Author : Agostino Prastaro
language : en
Publisher: World Scientific
Release Date : 2004-04-06

Quantized 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 2004-04-06 with Mathematics categories.

This book presents, for the first time, a systematic formulation of the geometric theory of noncommutative PDE's which is suitable enough to be used for a mathematical description of quantum dynamics and quantum field theory. A geometric theory of supersymmetric quantum PDE's is also considered, in order to describe quantum supergravity. Covariant and canonical quantizations of (super) PDE's are shown to be founded on the geometric theory of PDE's and to produce quantum (super) PDE's by means of functors from the category of commutative (super) PDE's to the category of quantum (super) PDE's. Global properties of solutions to (super) (commutative) PDE's are obtained by means of their integral bordism groups.

Mechanics

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Author : DS Mathur
language : en
Publisher: S. Chand Publishing
Release Date : 2000-10

Mechanics written by DS Mathur and has been published by S. Chand Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10 with Science categories.

The book presents a comprehensive study of important topics in Mechanics of pure and applied sciences. It provides knowledge of scalar and vector in optimum depth to make the students understand the concepts of Mechanics in simple, coherent and lucid manner and grasp its principles & theory. It caters to the requirements of students of B.Sc. Pass and Honours courses. Students of engineering disciplines and the ones aspiring for competitive exams such as AIME and others, will also find it useful for their preparations.

Computation And Visualization Of Geometric Partial Differential Equations

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Author : Christopher Tiee
language : en
Publisher: Lulu.com
Release Date : 2015-08-09

Computation And Visualization Of Geometric Partial Differential Equations written by Christopher Tiee and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-09 with Technology & Engineering categories.

This is an extended version of my PhD thesis which extends the theory of finite element exterior calculus (FEEC) to parabolic evolution equations. In the extended version, I explore some more precise visualizations of the defined quantities, as well as explain how the modern theory of functional analysis applies. In the main part, I extend the theory of approximating evolution equations in Euclidean space (using FEEC) to hypersurfaces. After these main results, I describe some possible extensions to nonlinear equations. A few appendices detail one of the original motivations for getting into this theory in the first place: canonical geometries given as steady state solutions and extremals of certain functionals.

Geometric Analysis And Nonlinear Partial Differential Equations

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Author : Stefan Hildebrandt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Geometric Analysis And Nonlinear Partial Differential Equations written by Stefan Hildebrandt 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 book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.

A Course Of Mathematical Analysis

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Author : Shanti Narayan | PK Mittal
language : en
Publisher: S. Chand Publishing
Release Date : 2005-03

A Course Of Mathematical Analysis written by Shanti Narayan | PK Mittal and has been published by S. Chand Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03 with Mathematics categories.

A Course of Mathematical Analysis

Interfaces Modeling Analysis Numerics

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Author : Eberhard Bänsch
language : en
Publisher: Springer Nature
Release Date : 2023-10-10

Interfaces Modeling Analysis Numerics written by Eberhard Bänsch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Mathematics categories.

These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization. We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.