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Author: Yoshikazu Giga
Publisher: Springer Science & Business Media
ISBN: 3764373911
Category : Mathematics
Languages : en
Pages : 270
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Book Description
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.
Author: Yoshikazu Giga
Publisher: Springer Science & Business Media
ISBN: 3764373911
Category : Mathematics
Languages : en
Pages : 270
Get Book Here
Book Description
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.
Author: Yoshikazu Giga
Publisher: Birkhäuser
ISBN: 9783764390082
Category : Mathematics
Languages : en
Pages : 264
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Book Description
Author: Kaïs Ammari
Publisher: Cambridge University Press
ISBN: 1108412300
Category : Mathematics
Languages : en
Pages : 205
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Book Description
The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.
Author: Yoshikazu Giga
Publisher:
ISBN:
Category :
Languages : en
Pages : 264
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Book Description
Author: Shu-Cheng Chang
Publisher: American Mathematical Soc.
ISBN: 0821833618
Category : Mathematics
Languages : en
Pages : 250
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Book Description
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.
Author: F. Bethuel
Publisher: Springer
ISBN: 3540488138
Category : Mathematics
Languages : en
Pages : 299
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Book Description
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.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 3642571867
Category : Mathematics
Languages : en
Pages : 347
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Book Description
At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.
Author: Stanley Osher
Publisher: Springer Science & Business Media
ISBN: 0387227466
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and Fedkiw; Osher and Fedkiw are internationally well-known researchers in this area
Author: Christian Klein
Publisher: Springer Science & Business Media
ISBN: 9783540285892
Category : Science
Languages : en
Pages : 274
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Book Description
Exact solutions to Einstein’s equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize interesting features of the theory. This volume studies the solutions to the Ernst equation associated to Riemann surfaces in detail. In addition, the book discusses the physical and mathematical aspects of this class analytically as well as numerically.
Author: Yasunori Maekawa
Publisher: Springer
ISBN: 3319667645
Category : Mathematics
Languages : en
Pages : 335
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Book Description
This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics, electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analysis and computation will find interest in this volume on theoretical study for nonlinear phenomena.
