By G. V. Alekseyev, A. Yu. Chebotarev (auth.), Prof. S. N. Antontsev, Prof. A. M. Khludnev, Prof. K.-H. Hoffmann (eds.)

A few extremum and unilateral boundary price difficulties in viscous hydrodynamics.- On axisymmetric movement of the fluid with a loose surface.- at the prevalence of singularities in axisymmetrical difficulties of hele-shaw type.- New asymptotic procedure for fixing of combined boundary worth problems.- a few effects at the thermistor problem.- New purposes of power the right way to parabolic and elliptic unfastened boundary problems.- A localized finite aspect technique for nonlinear water wave problems.- Approximate approach to research of ordinary oscillations of viscous incompressible liquid in container.- The classical Stefan challenge because the restrict case of the Stefan challenge with a kinetic situation on the unfastened boundary.- A mathematical version of oscillations power dissipation of viscous liquid in a tank.- life of the classical resolution of a two-phase multidimensional Stefan challenge on any finite time interval.- Asymptotic thought of propagation of nonstationary floor and inner waves over asymmetric bottom.- Multiparametric difficulties of two-dimensional loose boundary seepage.- Nonisothermal two-phase filtration in porous media.- particular answer of time-dependent unfastened boundary problems.- Nonequilibrium part transitions in frozen grounds.- method of variational inequalities bobbing up in nonlinear diffusion with section change.- touch viscoelastoplastic challenge for a beam.- program of a finite-element strategy to two-dimensional touch problems.- Computations of a fuel bubble movement in liquid.- Waves at the liquid-gas unfastened floor within the presence of the acoustic box in gas.- delicate bore in a two-layer fluid.- Numerical calculation of movable loose and make contact with barriers in difficulties of dynamic deformation of viscoelastic bodies.- at the canonical variables for two-dimensional vortex hydrodynamics of incompressible fluid.- in regards to the process with regularization for fixing the touch challenge in elasticity.- area evolution of tornado-like vortex core.- optimum form layout for parabolic process and two-phase Stefan problem.- Incompressible fluid flows with loose boundary and the tools for his or her research.- at the Stefan difficulties for the procedure of equations coming up within the modelling of liquid-phase epitaxy processes.- Stefan challenge with floor pressure as a restrict of the part box model.- The modelization of transformation part through the solution of an inclusion challenge with relocating boundary.- To the matter of creating susceptible recommendations in dynamic elastoplasticity.- The justification of the conjugate stipulations for the Euler’s and Darcy’s equations.- On an evolution challenge of thermo-capillary convection.- entrance monitoring tools for one-dimensional relocating boundary problems.- On Cauchy challenge for lengthy wave equations.- On fastened aspect (trial) equipment at no cost boundary problems.- Nonlinear idea of dynamics of a viscous fluid with a loose boundary within the means of a fantastic physique wetting.

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Additional info for Free Boundary Problems in Continuum Mechanics: International Conference on Free Boundary Problems in Continuum Mechanics, Novosibirsk, July 15–19,1991

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97-103. Gimatti. Existence of weak solutions for the nonstationary problem of the Jouhle heating of a conductor. Preprint, Universita di Pisa. Gimatti. A bound for the temperature in the thermistor problem. J. 15-22. Gimatti. 11712l. Prodi. 227-236. Friedman. Partial Differential equations of parabolic type, Prentice Hall, (1984). Trudinger. Elliptic partial differential equations of second order. Springer Verlag, (1985). Shillor. Stationary solution to the Thermistor problem. Apl. (To apear). Kohlrausch.

G. in (6), (7). e. , (5) in the context of phase change models, and in [8] in the context of planar deformable Hele-Shaw cells. In (4), (5) it has been stressed that two kinds of blow-up may occur: f or some T > O.. * ~tm* set) t-+T- = S(T*) > O. -00 and either (i) the solution cannot be continued (essential blow-up), (ii) the solution can be continued (non-essential blow-up). An example of the occurrence of (it) was provided. 10') (then g Pr is required to be continuous also for a continuous function in [O,T).

Has a global solution for 0 < n < N} > ~L. For N -+ N* the solutions to (~N) tend to a defined for any T (because the associated solution function is non-negative, being the monotone limit of non-negative functions). 0). 0) touches the free boundary in just one point, where we have a singularity. 1. Even in the case her) 0, one can exhibit an example of essential blow-up caused by a sui table Dirichlet datum prescribed on the fixed boundary r r o. This can be done following the lines of the proof in the Appendix of [8).

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