Energy Methods For Free Boundary Problems

Author : S.N. Antontsev,J.I. Diaz,S. Shmarev
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 41,9 Mb
Release : 2001-10-26
Category : Technology & Engineering
ISBN : 0817641238

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Energy Methods for Free Boundary Problems by S.N. Antontsev,J.I. Diaz,S. Shmarev Pdf

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

Author : Stanislav Nikolaevich Antont︠s︡ev,J. I. Díaz,S. I. Shmarev
Publisher : Birkhauser
Page : 329 pages
File Size : 49,6 Mb
Release : 2002
Category : Boundary value problems
ISBN : 3764341238

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Energy Methods for Free Boundary Problems by Stanislav Nikolaevich Antont︠s︡ev,J. I. Díaz,S. I. Shmarev Pdf

Author : S.N. Antontsev,J.I. Diaz,S. Shmarev
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461200918

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Energy Methods for Free Boundary Problems by S.N. Antontsev,J.I. Diaz,S. Shmarev Pdf

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

Author : S.N. Antontsev,J.I. Díaz,S.I. Shmarev
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400903371

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Energy Methods in Continuum Mechanics by S.N. Antontsev,J.I. Díaz,S.I. Shmarev Pdf

This volume contains the proceedings of the Workshop Energy Methods for Free Boundary Problems in Continuum Mechanics, held in Oviedo, Spain, from March 21 to March 23, 1994. It is well known that the conservation laws and the constitutive equations of Continuum Mechanics lead to complicated coupled systems of partial differential equations to which, as a rule, one fails to apply the techniques usually employed in the studies of scalar uncoupled equations such as, for instance, the maximum principle. The study of the qualitative behaviour of solutions of the systems re quires different techniques, among others, the so called, Energy Methods where the properties of some integral of a nonnegative function of one or several unknowns allow one to arrive at important conclusions on the envolved unknowns. This vol ume presents the state of the art in such a technique. A special attention is paid to the class of Free Boundary Problems. The organizers are pleased to thank the European Science Foundation (Pro gram on Mathematical treatment of free boundary problems), the DGICYT (Spain), the FICYT (Principado de Asturias, Spain) and the Universities of Oviedo and Complutense de Madrid for their generous financial support. Finally, we wish to thank Kluwer Academic Publishers for the facilities received for the publication of these Proceedings.

Author : Ioannis Athanasopoulos
Publisher : Routledge
Page : 366 pages
File Size : 55,5 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781351447140

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Free Boundary Problems by Ioannis Athanasopoulos Pdf

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.

Author : Antonio Fasano,Mario Primicerio
Publisher : Pitman Advanced Publishing Program
Page : 346 pages
File Size : 53,8 Mb
Release : 1983
Category : Boundary value problems
ISBN : UCSD:31822008735268

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Free Boundary Problems by Antonio Fasano,Mario Primicerio Pdf

Author : Isabel Narra Figueiredo,Lisa Santos
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 41,6 Mb
Release : 2007-01-11
Category : Mathematics
ISBN : 9783764377199

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Free Boundary Problems by Isabel Narra Figueiredo,Lisa Santos Pdf

This book collects refereed lectures and communications presented at the Free Boundary Problems Conference (FBP2005). These discuss the mathematics of a broad class of models and problems involving nonlinear partial differential equations arising in physics, engineering, biology and finance. Among other topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling, in fluid mechanics, in image processing, in financial mathematics or in computations for inter-scale problems.

Author : S.N. Antontsev,K.H. Hoffmann,A.M. Khludnev
Publisher : Birkhäuser
Page : 348 pages
File Size : 55,6 Mb
Release : 2013-03-07
Category : Science
ISBN : 9783034886277

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Free Boundary Problems in Continuum Mechanics by S.N. Antontsev,K.H. Hoffmann,A.M. Khludnev Pdf

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

Author : A. Bossavit,M. Fremond
Publisher : Unknown
Page : 334 pages
File Size : 54,5 Mb
Release : 1985
Category : Mathematics
ISBN : UCR:31210012400642

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Free Boundary Problems by A. Bossavit,M. Fremond Pdf

Author : J I Diaz,Juan Luis Vazquez,M A Herrero,Amable Linan
Publisher : CRC Press
Page : 236 pages
File Size : 44,5 Mb
Release : 1995-04-04
Category : Mathematics
ISBN : 0582256453

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Free Boundary Problems by J I Diaz,Juan Luis Vazquez,M A Herrero,Amable Linan Pdf

This research note consists of selected contributions from the 1993 International Conference on "Free Boundary Problems: Theory and Applications." These represent coherent and high-level research in the field of free boundary problems. Topics include mean curvature flows, phase transitions and material sciences, fluid mechanics and combustion problems.

Author : Marek Niezgodka,Pawel Strzelecki
Publisher : CRC Press
Page : 462 pages
File Size : 54,9 Mb
Release : 1996-11-25
Category : Mathematics
ISBN : 0582305934

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Free Boundary Problems, Theory and Applications by Marek Niezgodka,Pawel Strzelecki Pdf

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.

Author : J M Chadam,Helen Rasmussen
Publisher : CRC Press
Page : 264 pages
File Size : 53,6 Mb
Release : 1993-02-22
Category : Mathematics
ISBN : 0582087678

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Free Boundary Problems Involving Solids by J M Chadam,Helen Rasmussen Pdf

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.

Author : Stanislav Nikolaevich Antont︠s︡ev,Karl-Heinz Hoffmann,A. M. Khludnev
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 46,7 Mb
Release : 1992
Category : Mathematics
ISBN : 3764327847

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Free Boundary Problems in Continuum Mechanics by Stanislav Nikolaevich Antont︠s︡ev,Karl-Heinz Hoffmann,A. M. Khludnev Pdf

Some extremum and unilateral boundary value problems in viscous hydrodynamics.- On axisymmetric motion of the fluid with a free surface.- On the occurrence of singularities in axisymmetrical problems of hele-shaw type.- New asymptotic method for solving of mixed boundary value problems.- Some results on the thermistor problem.- New applications of energy methods to parabolic and elliptic free boundary problems.- A localized finite element method for nonlinear water wave problems.- Approximate method of investigation of normal oscillations of viscous incompressible liquid in container.- The classical Stefan problem as the limit case of the Stefan problem with a kinetic condition at the free boundary.- A mathematical model of oscillations energy dissipation of viscous liquid in a tank.- Existence of the classical solution of a two-phase multidimensional Stefan problem on any finite time interval.- Asymptotic theory of propagation of nonstationary surface and internal waves over uneven bottom.- Multiparametric problems of two-dimensional free boundary seepage.- Nonisothermal two-phase filtration in porous media.- Explicit solution of time-dependent free boundary problems.- Nonequilibrium phase transitions in frozen grounds.- System of variational inequalities arising in nonlinear diffusion with phase change.- Contact viscoelastoplastic problem for a beam.- Application of a finite-element method to two-dimensional contact problems.- Computations of a gas bubble motion in liquid.- Waves on the liquid-gas free surface in the presence of the acoustic field in gas.- Smooth bore in a two-layer fluid.- Numerical calculation of movable free and contact boundaries in problems of dynamic deformation of viscoelastic bodies.- On the canonical variables for two-dimensional vortex hydrodynamics of incompressible fluid.- About the method with regularization for solving the contact problem in elasticity.- Space evolution of tornado-like vortex core.- Optimal shape design for parabolic system and two-phase Stefan problem.- Incompressible fluid flows with free boundary and the methods for their research.- On the Stefan problems for the system of equations arising in the modelling of liquid-phase epitaxy processes.- Stefan problem with surface tension as a limit of the phase field model.- The modelization of transformation phase via the resolution of an inclusion problem with moving boundary.- To the problem of constructing weak solutions in dynamic elastoplasticity.- The justification of the conjugate conditions for the Euler's and Darcy's equations.- On an evolution problem of thermo-capillary convection.- Front tracking methods for one-dimensional moving boundary problems.- On Cauchy problem for long wave equations.- On fixed point (trial) methods for free boundary problems.- Nonlinear theory of dynamics of a viscous fluid with a free boundary in the process of a solid body wetting.

Author : Anvarbek Meirmanov,Oleg V. Galtsev,Reshat N. Zimin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 220 pages
File Size : 53,9 Mb
Release : 2017-09-11
Category : Mathematics
ISBN : 9783110546163

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Free Boundaries in Rock Mechanics by Anvarbek Meirmanov,Oleg V. Galtsev,Reshat N. Zimin Pdf

This monograph is concerned with free-boundary problems of partial differential equations arising in the physical sciences and in engineering. The existence and uniqueness of solutions to the Hele-Shaw problem are derived and techniques to deal with the Muskat problem are discussed. Based on these, mathematical models for the dynamics of cracks in underground rocks and in-situ leaching are developed. Contents Introduction The Hele–Shaw problem A joint motion of two immiscible viscous fluids Mathematical models of in-situ leaching Dynamics of cracks in rocks Elements of continuum mechanics

Author : Karl-Heinz Hoffmann
Publisher : Longman Scientific and Technical
Page : 464 pages
File Size : 46,5 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015019557027

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Free Boundary Problems by Karl-Heinz Hoffmann Pdf