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1
On the Lipschitz continuity of the solutions of a class of elliptic free boundary problems
100%
Lyaghfouri A.
Journal of Applied Analysis
|
2008
|
tom Vol. 14, nr 2
165-181
EN
In this article we prove local interior and boundary Lipschitz continuity of the solutions of a general class of elliptic free boundary problems in divergence form.
2
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.
3
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.
4
Content available remote Nonstationary Marangoni convection
80%
Wagner A.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 2
195-220
5
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.
6
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].
7
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
|
tom 79
|
nr 2
283-310
8
Differential inequalities for general fluid motions bounded by a free surface
80%
Zadrzyńska E. , Zajączkowski W. M.
Journal of Applied Analysis
|
2004
|
tom Vol. 10, nr 1
131-168
EN
We consider a motion of a viscous compressible heat conducting fluid of a fixed mass bounded by a free surface. For a local solution of equations describing such a motion we derive some energy-type inequalities which are necessary to prove the global existence of solutions.
9
Content available Analysis of a multiphase free boundary problem
80%
Abdelouahab A. , Bensid S.
Opuscula Mathematica
|
2024
|
tom Vol. 44, no. 5
631--649
EN
In this paper, we investigate a free boundary problem relevant in several applications, such as tumor growth models. Our problem is expressed as an elliptic equation involving discontinuous nonlinearities in a specified domain with a moving boundary. We establish the existence and uniqueness of solutions and provide a qualitative analysis of the free boundaries generated by the nonlinear term (inner boundaries). Furthermore, we analyze the dynamics of the outer region boundary. The final result demonstrates that under certain conditions, our problem is solvable in the neighborhood of a radial solution.
10
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.
11
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.
12
Content available remote On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface
73%
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
13
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.
14
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.
15
Content available remote 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.
16
Chemical attack in free boundary domains
60%
Clain S.
Journal of Applied Analysis
|
1999
|
tom Vol. 5, nr 1
35-58
EN
This paper presents a mathematical model for a chemical process used to machine cristal as glass or silica. A short physical description is presented from which we draw the mathematical model. We obtain a coupled parabolic equations system on a free boundary domain with a non-linear condition on the boundary. The existence and the uniqueness is proved in the one-dimensional case.
17
Content available remote Approximation of a Solidification Problem
60%
Aboulaich R. , Haggouch I. , Souissi A.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom Vol. 11, no 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 (Baiocci, 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.
18
Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting capillary fluids
51%
Zadrzyńska E. , Zajączkowski W. M.
Journal of Applied Analysis
|
2000
|
tom Vol. 6, nr 2
227-250
EN
In the paper the motion of a viscous compressible heat conducting capillary fluid in a domain bounded by a free surface is considered. We prove the local existence and uniqueness of a solution to a problem describing such a motion in anisotropic Sobolev-Slobodetskii spaces. This solution is such that the velocity and temperature belong to (wzór), and density to (wzór).
19
Content available remote Free boundary of journal bearing with spiral groove in HDD
51%
Lu P. , Xiao D. , Zhou G.
International Journal of Applied Mechanics and Engineering
|
2002
|
tom Vol. 7, no 3
859-874
EN
In a self-sealing journal bearing with spiral grooves, the bearing gap is not actually fully filled with lubricant. Specially at the seal interfaces, the so-called free boundary between the lubricant and ambient air is formed. A free boundary does not only influence the load-capacity and stability of a bearing, more importantly, it affects the bearing dynamic sealing capability. In this paper, an analytical model and numerical procedure is developed to investigate the free boundary of a journal bearing with spiral grooves. The simulation results are discussed on how the bearing parameters may affect free boundary and its impact on the bearing leakage. The approach establishes a base for precise calculation of performance parameters and optimization design of a journal bearing with spiral grooves in HDD.
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