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1
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A model of a radially symmetric cloud of self-attracting particles

100%
Nadzieja T.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 2
169-178
EN
We consider a parabolic equation which describes the gravitational interaction of particles. Existence of solutions and their convergence to stationary states are studied.
2
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Some personal remarks about applications of mathematics

100%
Nadzieja T.
Mathematica Applicanda
|
2014
|
tom 42
PL
Potrzeba rozwijania zastosowań matematyki spotyka się z akceptacją, zrozumieniem i życzliwym zainteresowaniem w środowisku matematyków. Świadczą o tym tworzone specjalizacje matematyka z ... lub zastosowania matematyki w ..., dopisywanie w pracach czysto matematycznych paru zdań lub nawet rozdziału o możliwych zastosowaniach uzyskanych wyników, często też referaty konferencyjne poprzedzone są wstępem omawiającym motywacje biologiczne, fizyczne czy chemiczne zajmowania się danym zagadnieniem. Organizuje się też wiele konferencji matematycznych poświęconych zastosowaniom matematyki w różnych dziedzinach nauk przyrodniczych lub ekonomicznych. Wszystko to daje fałszywy obraz bujnie rozwijających się zastosowań matematyki i ekspansji metod matematycznych w różnych dziedzinach nauk.
EN
Need to develop applications of mathematics meets with acceptance, understanding and sympathetic interest in the mathematicians world. Evidenced are by creation of the mathematics major with ... or the mathematics in ..., adding in a purely mathematical work of a few sentences or even a chapter on the possible applications of the results, conference papers often are preceded by an introductory discussion the motivations of the biological, physical or chemical character to deal with the issue. Organized a number of conferences devoted to mathematical applications of mathematics in various fields of natural sciences or economics. All this gives a false picture of lush developing applications of mathematics and expansion of mathematical methods in various fields of science.
3
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Growth and accretion of mass in an astrophysical model, II

64%
Biler P., Nadzieja T.
Applicationes Mathematicae
|
1995-1996
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tom 23
|
nr 3
351-361
EN
Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.
4
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Stationary solutions of aerotaxis equations

64%
Knosalla P., Nadzieja T.
Applicationes Mathematicae
|
2015
|
tom 42
|
nr 2-3
125-135
EN
We study the existence and uniqueness of the steady state in a model describing the evolution of density of bacteria and oxygen dissolved in water filling a capillary. The steady state is a stationary solution of a nonlinear and nonlocal problem which depends on the energy function and contains two parameters: the total mass of the colony of bacteria and the concentration (or flux) of oxygen at the end of the capillary. The existence and uniqueness of solutions depend on relations between these parameters and the maximum of the energy function.
5
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Evolution in a migrating population model

64%
Bąk W., Nadzieja T.
Applicationes Mathematicae
|
2012
|
tom 39
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nr 3
305-313
EN
We consider a model of migrating population occupying a compact domain Ω in the plane. We assume the Malthusian growth of the population at each point x ∈ Ω and that the mobility of individuals depends on x ∈ Ω. The evolution of the probability density u(x,t) that a randomly chosen individual occupies x ∈ Ω at time t is described by the nonlocal linear equation $u_t = ∫_Ω φ(y)u(y,t)dy - φ(x)u(x,t)$, where φ(x) is a given function characterizing the mobility of individuals living at x. We show that the asymptotic behaviour of u(x,t) as t → ∞ depends on the properties of φ in the vicinity of its zeros.
6
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Existence and nonexistence of solutions for a model of gravitational interaction of particles, I

64%
Biler P., Nadzieja T.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 2
319-334
EN
We study the existence of stationary and evolution solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles.
7
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A class of nonlocal parabolic problems occurring in statistical mechanics

64%
Biler P., Nadzieja T.
Colloquium Mathematicum
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1993
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tom 66
|
nr 1
131-145
EN
We consider parabolic equations with nonlocal coefficients obtained from the Vlasov-Fokker-Planck equations with potentials. This class of equations includes the classical Debye system from electrochemistry as well as an evolution model of self-attracting clusters under friction and fluctuations. The local in time existence of solutions to these equations (with no-flux boundary conditions) and properties of stationary solutions are studied.
8
Content available remote

Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

64%
Nadzieja T., Raczyński A.
Applicationes Mathematicae
|
2000
|
tom 27
|
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.
9
Content available remote

An elementary approach to nonexistence of solutions of linear parabolic equations

64%
Biler P., Nadzieja T.
Colloquium Mathematicum
|
2011
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tom 122
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nr 1
125-134
EN
This note presents an elementary approach to the nonexistence of solutions of linear parabolic initial-boundary value problems considered in the Feller test.
10
Content available remote

Nonlocal elliptic problems

64%
Krzywicki A., Nadzieja T.
Banach Center Publications
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2000
|
tom 52
|
nr 1
147-152
EN
Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem $-Δφ = M f(φ)/((∫_{Ω} f(φ))^p)$, $φ|_{𝜕Ω}=0$ are given.
11
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A singular radially symmetric problem in electrolytes theory

64%
Nadzieja T., Raczyński A.
Applicationes Mathematicae
|
1998-1999
|
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.
12
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Convergence to stationary solutions in a model of self-gravitating systems

64%
Guerra I., Nadzieja T.
Colloquium Mathematicum
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2003
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tom 98
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nr 1
39-47
EN
We study convergence of solutions to stationary states in an astrophysical model of evolution of clouds of self-gravitating particles.
13
Content available remote

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

52%
Biler P., Hilhorst D., Nadzieja T.
Colloquium Mathematicum
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1994
|
tom 67
|
nr 2
297-308
EN
We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.
14
Content available remote

Nonisothermal systems of self-attracting Fermi-Dirac particles

52%
Biler P., Nadzieja T., Stańczy R.
Banach Center Publications
|
2004
|
tom 66
|
nr 1
61-78
EN
The existence of stationary solutions and blow up of solutions for a system describing the interaction of gravitationally attracting particles that obey the Fermi-Dirac statistics are studied.
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