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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.
This textbook presents the classical topics of conduction heat transfer and extends the coverage to include chapters on perturbation methods, heat transfer in living tissue, and microscale conduction. This makes the book unique among the many published textbook on conduction heat transfer. Other noteworthy features of the book are: The material is organized to provide students with the tools to model, analyze and solve a wide range of engineering applications involving conduction heat transfer. Mathematical techniques are presented in a clear and simplified fashion to be used as instruments in obtaining solutions. The simplicity of one-dimensional conduction is used to drill students in the role of boundary conditions and to explore a variety of physical conditions that are of practical interest. Examples are carefully selected to illustrate the application of principles and the construction of solutions. Students are trained to follow a systematic problem solving methodology with emphasis on thought process, logic, reasoning and verification. Solutions to all examples and end-of-chapter problems follow an orderly problems solving approach. Extensive training material is available on the web The author provides an extensive solution manual for verifiable course instructors on request. Please send your request to [email protected]
Addressing various aspects of nonlinear partial differential equations, this volume contains papers and lectures presented at the Congress on Free boundary Problems, Theory and Application held in Zakopane, Poland in 1995. Topics include existence, uniqueness, asymptotic behavior, and regularity of solutions and interfaces.
Progress in different fields of mechanics, such as filtra tion theory, elastic-plastic problems, crystallization pro cesses, internal and surface waves, etc., is governed to a great extent by the advances in the study of free boundary problems for nonlinear partial differential equations. Free boundary problems form a scientific area which attracts attention of many specialists in mathematics and mechanics. Increasing interest in the field has given rise to the "International Conferences on Free Boundary Problems and Their Applications" which have convened, since the 1980s, in such countries as England, the United states, Italy, France and Germany. This book comprises the papers presented at the Interna tional Conference "Free Boundary Problems in Continuum Mechanics", organized by the Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, July 15-19, 1991, Novosibirsk, Russia. The scientific committee consisted of: Co-chairmen: K.-H. Hoffmann, L.V. Ovsiannikov S. Antontsev (Russia) J. Ockendon (UK) M. Fremond (France) L. Ovsiannikov (Russia) A. Friedman (USA) S. Pokhozhaev (Russia) K.-H. Hoffmann (Germany) M. Primicerio (Italy) A. Khludnev (Russia) V. Pukhnachov (Russia) V. Monakhov (Russia) Yu. Shokin (Russia) V. Teshukov (Russia) Our thanks are due to the members of the Scientific Com mittee, all authors, and participants for contributing to the success of the Conference. We would like to express special appreciation to N. Makarenko, J. Mal'tseva and T. Savelieva, Lavrentyev Institute of Hydrodynamics, for their help in preparing this book for publication
We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.
About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capillary convection in float-zone crystal growth. V. Rivkind considered numerical methods for solving coupled Navier-Stokes and Stefan equations. Besides of those invited lectures mentioned above there were 37 contributed papers presented. We shall briefly outline the topics of the contributed papers: Stefan like problems. Modelling, existence and uniqueness.
This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.
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.