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Variational approach to hyperbolic free boundary problems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Variational approach to hyperbolic free boundary problemsby Seiro Omata, Karel Svadlenka, Elliott Ginder.
Author:	Omata, Seiro.
other author:	Svadlenka, Karel.
Published:	Singapore :Springer Nature Singapore :2022.
Description:	ix, 94 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Hyperbolic.
Online resource:	https://doi.org/10.1007/978-981-19-6731-3
ISBN:	9789811967313$q(electronic bk.)

Variational approach to hyperbolic free boundary problems
Omata, Seiro.

Variational approach to hyperbolic free boundary problems[electronic resource] /by Seiro Omata, Karel Svadlenka, Elliott Ginder. - Singapore :Springer Nature Singapore :2022. - ix, 94 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

Chapter 1. Introduction -- Chapter 2.Physical motivation -- Chapter 3.Discrete Morse flow -- Chapter 4. Discrete Morse flow with free boundary -- Chapter 5.Energy-preserving discrete Morse flow -- Chapter 6.Numerical examples and applications.

This volume is devoted to the study of hyperbolic free boundary problems possessing variational structure. Such problems can be used to model, among others, oscillatory motion of a droplet on a surface or bouncing of an elastic body against a rigid obstacle. In the case of the droplet, for example, the membrane surrounding the fluid in general forms a positive contact angle with the obstacle, and therefore the second derivative is only a measure at the contact free boundary set. We will show how to derive the mathematical problem for a few physical systems starting from the action functional, discuss the mathematical theory, and introduce methods for its numerical solution. The mathematical theory and numerical methods depart from the classical approaches in that they are based on semi-discretization in time, which facilitates the application of the modern theory of calculus of variations.

ISBN: 9789811967313$q(electronic bk.)

Standard No.: 10.1007/978-981-19-6731-3doiSubjects--Topical Terms:

199039
Differential equations, Hyperbolic.

LC Class. No.: QA377

Dewey Class. No.: 515.3535

Variational approach to hyperbolic free boundary problems
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520 $a This volume is devoted to the study of hyperbolic free boundary problems possessing variational structure. Such problems can be used to model, among others, oscillatory motion of a droplet on a surface or bouncing of an elastic body against a rigid obstacle. In the case of the droplet, for example, the membrane surrounding the fluid in general forms a positive contact angle with the obstacle, and therefore the second derivative is only a measure at the contact free boundary set. We will show how to derive the mathematical problem for a few physical systems starting from the action functional, discuss the mathematical theory, and introduce methods for its numerical solution. The mathematical theory and numerical methods depart from the classical approaches in that they are based on semi-discretization in time, which facilitates the application of the modern theory of calculus of variations.
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