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＜電子ブック＞
Variational Approach to Hyperbolic Free Boundary Problems / by Seiro Omata, Karel Svadlenka, Elliott Ginder
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2022.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	IX, 94 p. 1 illus : online resource
著者標目	*Omata, Seiro author Svadlenka, Karel author Ginder, Elliott author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Functional analysis FREE:Differential Equations FREE:Calculus of Variations and Optimization FREE:Functional Analysis
一般注記	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. HTTP:URL=https://doi.org/10.1007/978-981-19-6731-3

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