Variational Approach to Hyperbolic Free Boundary Problems (SpringerBriefs in Mathematics) - Softcover

Omata, Seiro; Svadlenka, Karel; Ginder, Elliott

 
9789811967306: Variational Approach to Hyperbolic Free Boundary Problems (SpringerBriefs in Mathematics)
Softcover
ISBN 10: 981196730X ISBN 13: 9789811967306
Publisher: Springer, 2022

Synopsis

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. 

"synopsis" may belong to another edition of this title.

About the Author

Seiro Omata was born in 1957 in Tokyo and received his Master and PhD degrees from Keio University. Since 1994 he has been working at Kanazawa University, becoming Full Professor in 2004. His research focuses on nonlinear evolutionary PDEs, including variational and free boundary problems, numerical analysis and applied analysis spanning numerous topics from fluid dynamics to mathematical finance. He devoted himself to the development of mathematics through the Mathematical Society of Japan, being invited as plenary speaker at its annual meeting in 2014 and serving as the chair of annual meeting in 2019. 


Karel Svadlenka received his PhD in mathematics from Kanazawa University, Japan and from Charles University in Prague, Czech Republic, and has been an Associate Professor at the Department of Mathematics, Graduate School of Science, Kyoto University, Japan since 2014. His research interests include calculus variations, nonlinear partial differential equations, numerical analysis, and mathematical modeling. 

Elliott Ginder is a Professor at Meiji University in the School of Interdisciplinary Mathematical Sciences. An Aries, he enjoys applied mathematics, especially topics involving interfacial motions, and the calculus of variations. 

From the Back Cover

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. 

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2022
Language
English
ISBN 10 
981196730X
ISBN 13 
9789811967306
Binding
Paperback
Edition number
1
Number of pages
104

Other Popular Editions of the Same Title

9789811967320: Variational Approach to Hyperbolic Free Boundary Problems

Featured Edition

ISBN 10:  9811967326 ISBN 13:  9789811967320
Publisher: Springer, 2022
Softcover