Free Boundary Problems In Continuum Mechanics: International Conference On Free Boundary Problems In Continuum Mechanics, Novosibirsk, July 15-19,1991 (international Series Of Numerical Mathematics)

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. Front Matter....Pages I-IX Some Extremum and Unilateral Boundary Value Problems in Viscous Hydrodynamics....Pages 1-11 On Axisymmetric Motion of the Fluid with a Free Surface....Pages 13-21 On the Occurrence of Singularities in Axisymmetrical Problems of Hele-Shaw Type....Pages 23-38 New Asymptotic Method for Solving of Mixed Boundary Value Problem....Pages 39-45 Some Results on the Thermistor Problem....Pages 47-57 New Applications of Energy Methods to Parabolic and Elliptic Free Boundary Problems....Pages 59-65 A Localized Finite Element Method for Nonlinear Water Wave Problems....Pages 67-74 Approximate Method of Investigation of Normal Oscillations of Viscous Incompressible Liquid in Container....Pages 75-82 The Classical Stefan Problem as the Limit Case of the Stefan Problem with a Kinetic Condition at the Free Boundary....Pages 83-90 A Mathematical Model of Oscillations Energy Dissipation of Viscous Liquid in a Tank....Pages 91-96 Existence of the Classic Solution of a Two Phase Multidimensional Stefan Problem on Any Finite Time Interval....Pages 97-103 Asymptotic Theory of Propagation of Nonstationary Surface and Internal Waves over Uneven Bottom....Pages 105-111 Multiparametric Problems of Two-Dimensional Free-Boundary Seepage....Pages 113-119 Nonisothermal Two-Phase Filtration in Porous Media....Pages 121-130 Explicit Solution of Time-Dependent Free Boundary Problems....Pages 131-140 Nonequilibrium Phase Transitions in Frozen Grounds....Pages 141-147 System of Variational Inequalities Arising in Nonlinear Diffusion with Phase Change....Pages 149-157 Contact Viscoelastoplastic Problem for a Beam....Pages 159-166 Application of a Finite-Element Method to Two-Dimensional Contact Problems....Pages 167-177 Computations of a Gas Bubble Motion in Liquid....Pages 179-185 Waves on the Liquids-Gas Free Surface in the Presence of the Acoustic Field in Gas....Pages 187-194 Smooth Bore in a Two-Layer Fluid....Pages 195-204 Numerical Calculation of Movable Free and Contact Boundaries in Problems of Dynamics Deformation of Viscoelastic Bodies....Pages 205-213 On the Canonical Variables for Two-Dimensional Vortex Hydrodynamics of Incompressible Fluid....Pages 215-221 About the Method with Regularization for Solving the Contact Problem in Elasticity....Pages 223-228 Space Evolution of Tornado-Like Vortex Core....Pages 229-237 Optimal Shape Design for Parabolic System and Two-Phase Stefan Problem....Pages 239-244 Incompressible Fluid Flows with Free Boundary and the Methods for their Research....Pages 245-252 On the Stefan Problems for the System of Equations Arising in the Modelling of Liquid-Phase Epitaxy Processes....Pages 253-262 Stefan Problem with Surface Tension as a Limit of the Phase Field Model....Pages 263-270 The Modelization of Transformation Phase Via the Resolution of an Inclusion Problem with Moving Boundary....Pages 271-281 To the Problem of Constructing Weak Solutions in Dynamic Elastoplasticity....Pages 283-291 The Justification of the Conjugate Conditions for the Euler’s and Darcy’s Equations....Pages 293-300 On an Evolution Problem of Thermocapillary Convection....Pages 301-317 Front Tracking Methods for One-Dimensional Moving Boundary Problems....Pages 319-329 On Cauchy Problem for Long Wave Equations....Pages 331-338 On Fixed Point (Trial) Methods for Free Boundary Problems....Pages 339-350 Nonlinear Theory of Dynamics of a Viscous Fluid with a Free Boundary in the Process of a Solid Body Wetting....Pages 351-358 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