The Curve Shortening Problem

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The Curve Shortening Problem

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Author : Kai-Seng Chou
language : en
Publisher: CRC Press
Release Date : 2001-03-06

The Curve Shortening Problem written by Kai-Seng Chou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-06 with Mathematics categories.

Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature. For the first time, The Curve Shortening Problem collects and illuminates those results in a comprehensive, rigorous, and self-contained account of the fundamental results. The a

Nonlinear Diffusion Equations And Their Equilibrium States 3

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Author : N.G Lloyd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Diffusion Equations And Their Equilibrium States 3 written by N.G Lloyd 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.

Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.

Calculus Of Variations Applications And Computations

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Author : C Bandle
language : en
Publisher: CRC Press
Release Date : 1995-04-26

Calculus Of Variations Applications And Computations written by C Bandle and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-26 with Mathematics categories.

This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.

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.

Lectures On Mean Curvature Flows

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Author : Xi-Ping Zhu
language : en
Publisher: American Mathematical Soc.
Release Date :

Lectures On Mean Curvature Flows written by Xi-Ping Zhu 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 with Mathematics categories.

Calculus Of Variations And Geometric Evolution Problems

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Author : F. Bethuel
language : en
Publisher: Springer
Release Date : 2006-11-14

Calculus Of Variations And Geometric Evolution Problems written by F. Bethuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.

Lecture Notes On Mean Curvature Flow

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Author : Carlo Mantegazza
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-28

Lecture Notes On Mean Curvature Flow written by Carlo Mantegazza 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 2011-07-28 with Mathematics categories.

This book is an introduction to the subject of mean curvature flow of hypersurfaces with special emphasis on the analysis of singularities. This flow occurs in the description of the evolution of numerous physical models where the energy is given by the area of the interfaces. These notes provide a detailed discussion of the classical parametric approach (mainly developed by R. Hamilton and G. Huisken). They are well suited for a course at PhD/PostDoc level and can be useful for any researcher interested in a solid introduction to the technical issues of the field. All the proofs are carefully written, often simplified, and contain several comments. Moreover, the author revisited and organized a large amount of material scattered around in literature in the last 25 years.

The Schwarz Function And Its Applications

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Author : Philip J. Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 1974-12-31

The Schwarz Function And Its Applications written by Philip J. Davis 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 1974-12-31 with Mathematics categories.

H. A. Schwarz showed us how to extend the notion of reflection in straight lines and circles to reflection in an arbitrary analytic arc. Notable applications were made to the symmetry principle and to problems of analytic continuation. Reflection, in the hands of Schwarz, is an antianalytic mapping. By taking its complex conjugate, we arrive at an analytic function that we have called here the Schwarz Function of the analytic arc. This function is worthy of study in its own right and this essay presents such a study. In dealing with certain familiar topics, the use of the Schwarz Function lends a point of view, a clarity and elegance, and a degree of generality which might otherwise be missing. It opens up a line of inquiry which has yielded numerous interesting things in complex variables; it illuminates some functional equations and a variety of iterations which interest the numerical analyst. The perceptive reader will certainly find here some old wine in relabelled bottles. But one of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems. Means become ends; the medium rapidly becomes the message. This book is not wholly self-contained. Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable.

Nonlinear Partial Differential Equations In Differential Geometry

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Author : Robert Hardt
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Nonlinear Partial Differential Equations In Differential Geometry written by Robert Hardt 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 1996 with Mathematics categories.

The lecture notes from a July 1992 minicourse in Park City, Utah, for graduate students and research mathematicians in differential geometry and partial differential equations. They survey the current state of such aspects as the Moser-Trudinger inequality and its applications to some problems in conformal geometry, the effect of curvature on the behavior of harmonic functions and mapping, and singularities of geometric variational problems. No index. Annotation copyright by Book News, Inc., Portland, OR

Mathematical Systems Theory In Biology Communications Computation And Finance

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

Mathematical Systems Theory In Biology Communications Computation And Finance written by Joachim Rosenthal 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 Science categories.

Mathematical systems theory is a vibrant research area in its own right. The theory has an impact in numerous applications areas including aeronautics, biological systems, chemical engineering, communication systems, financial engineering and robotics to name just a few. This volume contains survey and research articles by some of the leading researchers in mathematical systems theory. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists. The articles contained in this volume are from those presented as plenary lectures, invited one hour lectures and minisymposia at the 15th International Symposium on the Mathematical Theory of Networks and Systems held at the University of Notre Dame, August 12-16, 2002.