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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Existence and regularity of solutions of some elliptic system in domains with edges

100%
Zajączkowski W. M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction.......................................................................5 2. Notation and auxiliary results............................................9 3. Statement of the problem (1.1)-(1.3)..............................20 4. The problem (3.14).........................................................22 5. Auxiliary results in $D_ϑ$...............................................34 6. Existence of solutions of (3.14) in $H^k_μ(D_ϑ)$............41 7. Green function................................................................52 8. The problem (3.13) in $L^k_{p,μ}(D_ϑ)$ spaces............59 9. The problem (3.13) in weighted Hölder spaces...............67 10. The problem (1.1)-(1.3) in a bounded domain Ω..........75 Appendix. The distinguished case: μ+2/p∊ℤ......................86 References.........................................................................90
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On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface

100%
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
3
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$L_∞$-estimate for solutions of nonlinear parabolic systems

95%
Zajączkowski W. M.
Banach Center Publications
|
1996
|
tom 33
|
nr 1
465-490
EN
We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_∞$-estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_∞$-estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_∞$-estimates are obtained by the Di Benedetto methods.
4
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$L_∞$-estimates for solutions of nonlinear parabolic systems with gradient linear growth

95%
Zajączkowski W. M.
Banach Center Publications
|
1996
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tom 33
|
nr 1
491-501
EN
Existence of weak solutions and an $L_∞$-estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_∞$-estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.
5
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On the existence and regularity of solutions to the problem of transmission

95%
Zajączkowski W. M.
Banach Center Publications
|
1990
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tom 24
|
nr 1
269-292
6
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On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary

60%
Zadrzyńska E., Zajączkowski W. M.
Colloquium Mathematicum
|
1999
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tom 79
|
nr 2
283-310
7
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Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids

60%
Zadrzyńska E., Zajączkowski W. M.
Applicationes Mathematicae
|
1998-1999
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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.
8
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Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics

60%
Rencławowicz J., Zajączkowski W. M.
Applicationes Mathematicae
|
1998-1999
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tom 25
|
nr 2
221-252
EN
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method of successive approximations.
9
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On global motion of a compressible barotropic viscous fluid with boundary slip condition

60%
Kobayashi T., Zajączkowski W. M.
Applicationes Mathematicae
|
1999
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tom 26
|
nr 2
159-194
EN
Global-in-time existence of solutions for equations of viscous compressible barotropic fluid in a bounded domain Ω ⊂ $ℝ^3$ with the boundary slip condition is proved. The solution is close to an equilibrium solution. The proof is based on the energy method. Moreover, in the $L_2$-approach the result is sharp (the regularity of the solution cannot be decreased) because the velocity belongs to $H^{2+α,1+α/2}(Ω × ℝ_+)$ and the density belongs to $H^{1+α,1/2+α/2}(Ω× ℝ_+)$, α ∈ (1/2,1).
10
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On diffused-interface models of shape memory alloys

36%
Pawłow I., Zajączkowski W. M.
Control and Cybernetics
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2003
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tom 32
|
nr 3
629-658
11
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Preface, Contents

31%
Janeczko S., Zajączkowski W. M., Ziemian B.
Banach Center Publications
|
1996
|
tom 33
|
nr 1
1-8
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