Fourth Order Geometric Evolution Equations

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Fourth Order Geometric Evolution Equations

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Author : Glen Edward Wheeler
language : en
Publisher:
Release Date : 2009

Fourth Order Geometric Evolution Equations written by Glen Edward Wheeler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Calculus of variations categories.

Geometric Evolution Equations

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Author : Shu-Cheng Chang
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Geometric Evolution Equations written by Shu-Cheng Chang 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 2005 with Mathematics categories.

The Workshop on Geometric Evolution Equations was a gathering of experts that produced this comprehensive collection of articles. Many of the papers relate to the Ricci flow and Hamilton's program for understanding the geometry and topology of 3-manifolds. The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solution of Thurston's Geometrization Conjecture and the Poincare Conjecture. Yet applying the method poses serious technical problems. Contributors to this volume explain some of these issues and demonstrate a noteworthy deftness in the handling of technical areas. Various topics in geometric evolution equations and related fields are presented. Among other topics covered are minimal surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kahler-Ricci flow, function theory on Kahler manifolds, flows of plane curves, convexity estimates, and the Christoffel-Minkowski problem. The material is suitable for graduate students and researchers interested in geometric analysis and connections to topology. Related titles of interest include The Ricci Flow: An Introduction.

Geometric Evolution Equations

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Author : Stacey E. Chastain
language : en
Publisher:
Release Date : 2000

Geometric Evolution Equations written by Stacey E. Chastain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.

A Concise Introduction To Geometric Numerical Integration

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Author : Sergio Blanes
language : en
Publisher: CRC Press
Release Date : 2017-11-22

A Concise Introduction To Geometric Numerical Integration written by Sergio Blanes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

Surface Evolution Equations

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Author : Yoshikazu Giga
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Surface Evolution Equations written by Yoshikazu Giga 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 2006-03-30 with Mathematics categories.

This book presents a self-contained introduction to the analytic foundation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in many applications, such as material sciences, image processing and differential geometry. The goal is to introduce a generalized notion of solutions allowing singularities, and to solve the initial-value problem globally-in-time in a generalized sense. Various equivalent definitions of solutions are studied. Several new results on equivalence are also presented. Moreover, structures of level set equations are studied in detail. Further, a rather complete introduction to the theory of viscosity solutions is contained, which is a key tool for the level set approach. Although most of the results in this book are more or less known, they are scattered in several references, sometimes without proofs. This book presents these results in a synthetic way with full proofs. The intended audience are graduate students and researchers in various disciplines who would like to know the applicability and detail of the theory as well as its flavour. No familiarity with differential geometry or the theory of viscosity solutions is required. Only prerequisites are calculus, linear algebra and some basic knowledge about semicontinuous functions.

Evolution Equations

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Author : David Ellwood
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-26

Evolution Equations written by David Ellwood 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 2013-06-26 with Mathematics categories.

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).

First Order Geometric Evolutions And Semilinear Evolution Equations

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Author :
language : en
Publisher:
Release Date : 2004

First Order Geometric Evolutions And Semilinear Evolution Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

The primary aim of this Ph. D. thesis is to unify the definition of "solution" for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems whose components have their origins in diverse applications. The analytical touchstone of the general character consists of (1.) a semilinear evolution equation in a reflexive Banach space and (2.) a first-order geometric evolution, i.e. a time-dependent compact subset of R^n, whose deformation depends on nonlocal properties of normal cones at the boundary. (No inclusion principle is assumed.) Taking up the widespread idea of derivatives as first-order approximations, distance functions (maybe in a generalized sense) are required and essentially the only tool to use for a general approach beyond vector spaces. Here two concepts are presented, both of which are based on generalizing the mutational equations of Jean-Pierre Aubin (in metric spaces) to a set with a countable family of so-called ostensible metrics (that need not be symmetric).

Geometric Evolution Equations And P Harmonic Theory With Applications In Differential Geometry

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Author : Junfang Li
language : en
Publisher:
Release Date : 2006

Geometric Evolution Equations And P Harmonic Theory With Applications In Differential Geometry written by Junfang Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations, Partial categories.

Fully Variational Lagrangian Discretizations For Second And Fourth Order Evolution Equations

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Author : Horst Osberger
language : en
Publisher:
Release Date : 2015

Fully Variational Lagrangian Discretizations For Second And Fourth Order Evolution Equations written by Horst Osberger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

Evolution Equations With A Complex Spatial Variable

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Author : Ciprian G Gal
language : en
Publisher: World Scientific
Release Date : 2014-03-18

Evolution Equations With A Complex Spatial Variable written by Ciprian G Gal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-18 with Mathematics categories.

This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black-Merton-Scholes, Schrödinger and Korteweg-de Vries equations.The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought.For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane.