Surface evolution equations a level set approach Yoshikazu Giga, Qing Liu

Format:

Book

Author/Creator:

Giga, Yoshikazu, author.

Liu, Qing (Of Okinawa Kagaku Gijutsu Daigakuin Daigaku), author.

Series:

Monographs in mathematics ; v. 99.

Monographs in mathematics 2296-4886 volume 99

Language:

English

Subjects (All):

Evolution equations.

Hamilton-Jacobi equations.

Curves, Algebraic.

Differential equations, Parabolic.

Physical Description:

1 online resource

Edition:

Second edition

Place of Publication:

Cham, Switzerland Birkhäuser [2026]

Summary:

"This monograph 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. For the Second Edition, new chapters have been added that describe a recent approach to surface evolution equations based on deterministic discrete two-person games. This game-theoretic interpretation is used to discuss the fattening phenomenon for the curvature flow equation and to provide an alternative proof for convexity preserving properties. This text is suitable for applied researchers who would like to know the detail of the theory, as well as its flavor; it is also suitable for graduate students interested in the field. Prerequisites include calculus, linear algebra, and some familiarity with semicontinuous functions. Familiarity with differential geometry and the theory of viscosity solutions is not required"-- Springer Nature Link

Contents:

Surface evolution equations

Viscosity solutions

Comparison principle

Classical level set method

Set-theoretic approach

Deterministic game interpretations

Applications of game-theoretic approach

Notes:

Previous edition published in 2006

Includes bibliographical references and index

Online resource; title from PDF title page (Springer Nature Link, viewed July 16, 2026)

Other Format:

Print version Giga, Yoshikazu Surface evolution equations

ISBN:

9783032203038

3032203031

OCLC:

1603213699

Access Restriction:

Restricted for use by site license