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1
Content available remote

On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface

100%
Zadrzyńska E., Zajączkowski W.
Annales Polonici Mathematici
|
1995
|
tom 61
|
nr 2
141-188
EN
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat conducting fluid. The inequality is essential in proving the global existence of solutions.
2
Content available remote

On local motion of a general compressible viscous heat conducting fluid bounded by a free surface

80%
Zadrzyńska E., Zajączkowski W.
Annales Polonici Mathematici
|
1994
|
tom 59
|
nr 2
133-170
EN
The motion of a viscous compressible heat conducting fluid in a domain in ℝ³ bounded by a free surface is considered. We prove local existence and uniqueness of solutions in Sobolev-Slobodetskiĭ spaces in two cases: with surface tension and without it.
3
Content available remote

On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface

80%
Zadrzyńska E., Zajączkowski W.
Annales Polonici Mathematici
|
1996-1997
|
tom 65
|
nr 1
23-53
EN
We derive a global differential inequality for solutions of a free boundary problem for a viscous compressible heat concluding capillary fluid. The inequality is essential in proving the global existence of solutions.
4
Content available remote

On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary

80%
Zadrzyńska E., Zajączkowski W. M.
Colloquium Mathematicum
|
1999
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tom 79
|
nr 2
283-310
5
Content available remote

Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids

80%
Zadrzyńska E., Zajączkowski W. M.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 2
179-220
EN
The local existence and the uniqueness of solutions for equations describing the motion of viscous compressible heat-conducting fluids in a domain bounded by a free surface is proved. First, we prove the existence of solutions of some auxiliary problems by the Galerkin method and by regularization techniques. Next, we use the method of successive approximations to prove the local existence for the main problem.
6
Content available remote

Nonstationary Marangoni convection

80%
Wagner A.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 2
195-220
7
Content available remote

Existence of local solutions for free boundary problems for viscous compressible barotropic fluids

80%
Zajączkowski W.
Annales Polonici Mathematici
|
1994-1995
|
tom 60
|
nr 3
255-287
EN
We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].
8
Content available remote

On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary

80%
Zadrzyńska E.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 4
489-511
EN
The motion of a fixed mass of a viscous compressible heat conducting capillary fluid is examined. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global-in-time solution which is close to the constant state for any moment of time. Moreover, we present an analogous result for the case of a barotropic viscous compressible fluid.
9
Content available remote

On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface

72%
Zajączkowski W. M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
We consider the motion of a viscous compressible barotropic fluid in $ℝ^3$ bounded by a free surface which is under constant exterior pressure. For a given initial density, initial domain and initial velocity we prove the existence of local-in-time highly regular solutions. Next assuming that the initial density is sufficiently close to a constant, the initial pressure is sufficiently close to the external pressure, the initial velocity is sufficiently small and the external force vanishes we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.
XX
CONTENTS 1. Introduction.......................................5 2. Global estimates and relations........11 3. Local existence...............................16 4. Global differential inequality............44 5. Korn inequality................................81 6. Global existence.............................89 References.......................................100
10
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A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process

70%
Roliński T.
Annales Polonici Mathematici
|
1995
|
tom 61
|
nr 3
195-223
EN
We investigate the behaviour of the meniscus of a drop of liquid aluminium in the neighbourhood of a state of equilibrium under the influence of weak electromagnetic forces. The mathematical model comprises both Maxwell and Navier-Stokes equations in 2D. The meniscus is governed by the Young-Laplace equation, the data being the jump of the normal stress. To show the existence and uniqueness of the solution we use the classical implicit function theorem. Moreover, the differentiability of the operator solving this problem is established.
11
Content available remote

Approximation of a solidification problem

70%
Aboulaïch R., Haggouch I., Souissi A.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 4
921-955
EN
A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocchi, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al., 1991; Saguez, 1980), or a control problem (El Bagdouri, 1987; Peneau, 1995; Saguez, 1980). In the present work, we provide a new formulation leading to a shape optimization problem. For a semidiscretization in time, we consider an Euler scheme. Under some restrictions related to stability conditions, we prove an L^2 -rate of convergence of order 1 for the temperature. In the last part, we study the existence of an optimal shape, compute the shape gradient, and suggest a numerical algorithm to approximate the free boundary. The numerical results obtained show that this method is more efficient compared with the others.
12
Content available remote

On local motion of a compressible barotropic viscous fluid bounded by a free surface

70%
Zajączkowski W. M.
Banach Center Publications
|
1992
|
tom 27
|
nr 2
511-553
EN
We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the existence time.
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