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1
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Existence of solutions for a model of self-gravitating particles with external potential

100%
Raczyński A.
Banach Center Publications
|
2004
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tom 66
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nr 1
263-275
EN
We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.
2
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A model of evolution of temperature and density of ions in an electrolyte

100%
Raczyński A.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 2
225-241
EN
We study existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions. In this model the evolution of temperature is also taken into account. For stationary states the existence of an external potential is also assumed.
3
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On a nonlocal elliptic problem

100%
Raczyński A.
Applicationes Mathematicae
|
1999
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tom 26
|
nr 1
107-119
EN
We study stationary solutions of the system $u_t = ∇ ((m-1)/m ∇u^m + u∇φ)$, m => 1, Δφ = ±u, defined in a bounded domain Ω of $ℝ^n$. The physical interpretation of the above system comes from the porous medium theory and semiconductor physics.
4
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Weak-$L^{p}$ solutions for a model of self-gravitating particles with an external potential

100%
Raczyński A.
Studia Mathematica
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2007
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tom 179
|
nr 3
199-216
EN
The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak-$L^{p}$ spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.
5
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Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

64%
Nadzieja T., Raczyński A.
Applicationes Mathematicae
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2000
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tom 27
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nr 4
465-473
EN
We consider the following problem: $ΔΦ = ± {M οver \int_{Ω} e^{- Φ/Θ}} e^{- Φ/Θ}, E = MΘ ∓ {1οver2}\int_{Ω} |∇Φ|^2, Φ|_{\partial Ω} = 0,$ where Φ: Ω ⊂ $ℝ^n$ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.
6
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A singular radially symmetric problem in electrolytes theory

64%
Nadzieja T., Raczyński A.
Applicationes Mathematicae
|
1998-1999
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tom 25
|
nr 1
101-112
EN
Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.
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