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

100%
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.
2
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A class of nonlocal parabolic problems occurring in statistical mechanics

100%
Biler P., Nadzieja T.
Colloquium Mathematicum
|
1993
|
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.
3
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Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

100%
Biler P., Hilhorst D., Nadzieja T.
Colloquium Mathematicum
|
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.
4
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Nonlinear multivalued boundary value problems

63%
Bader R., Papageorgiou N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
|
tom 21
|
nr 1
127-148
EN
In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $domA ≠ ℝ^{N}$ and $domA = ℝ^{N}$, with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.
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