Variational Principles And Free Boundary Problems
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Variational Principles And Free Boundary Problems
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Author : Avner Friedman
language : en
Publisher:
Release Date : 1988
Variational Principles And Free Boundary Problems written by Avner Friedman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the standard theory of elliptic and parabolic operators make this treatment readable for engineers, students, and nonspecialists alike. The text's first two chapters can be used for a single-semester graduate course in variational inequalities or partial differential equations. The succeeding chapters -- covering jets and cavities, variational problems with potentials, and free-boundary problems not in variational form -- are more specialized and self-contained. Readers who have mastered chapters 1 and 2 will be able to conduct research on the problems explored in subsequent chapters. Bibliographic remarks conclude each chapter, along with several problems and exercises.
Variational Principles And Free Boundary Problems
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Author :
language : en
Publisher:
Release Date : 1988
Variational Principles And Free Boundary Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Variational And Free Boundary Problems
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Author : Avner Friedman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational And Free Boundary Problems written by Avner Friedman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries. " The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un known domain, an additional condition must be prescribed on the free boundary. A classical example is the Stefan problem of melting of ice; here the temperature sat isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera ture within the water. Some free boundary problems lend themselves to variational formulation.
Variational And Free Boundary Problems
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Author : Avner Friedman
language : en
Publisher: Springer
Release Date : 1993-10-22
Variational And Free Boundary Problems written by Avner Friedman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-22 with Science categories.
This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries. " The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un known domain, an additional condition must be prescribed on the free boundary. A classical example is the Stefan problem of melting of ice; here the temperature sat isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera ture within the water. Some free boundary problems lend themselves to variational formulation.
Variational Problems With Concentration
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Author : Martin F. Bach
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Variational Problems With Concentration written by Martin F. Bach and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and the free boundary. The corresponding plots are highlights of this book.
Variational And Quasivariational Inequalities
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Author : C. Baiocchi
language : en
Publisher: John Wiley & Sons
Release Date : 1984
Variational And Quasivariational Inequalities written by C. Baiocchi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Complementary Variational Principles
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Author : A. M. Arthurs
language : en
Publisher: Oxford University Press, USA
Release Date : 1980
Complementary Variational Principles written by A. M. Arthurs and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations
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Author : M. A. Lavrent’ev
language : en
Publisher: Courier Dover Publications
Release Date : 2016-01-14
Variational Methods For Boundary Value Problems For Systems Of Elliptic Equations written by M. A. Lavrent’ev and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-14 with Mathematics categories.
Famous monograph by a distinguished mathematician presents an innovative approach to classical boundary value problems. The treatment employs the basic scheme first suggested by Hilbert and developed by Tonnelli. 1963 edition.
Variational Approach To Hyperbolic Free Boundary Problems
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Author : Seiro Omata
language : en
Publisher: Springer Nature
Release Date : 2022-11-28
Variational Approach To Hyperbolic Free Boundary Problems written by Seiro Omata and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-28 with Mathematics categories.
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.
Free Boundary Problems
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Author : Ioannis Athanasopoulos
language : en
Publisher: Routledge
Release Date : 2019-11-11
Free Boundary Problems written by Ioannis Athanasopoulos and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.