Displaying similar documents to “Global solutions for a problem modeling the dynamics of a system of self-gravitating Brownian particles”

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

Andrzej Raczyński (2004)

Banach Center Publications

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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.

The Cauchy problem and self-similar solutions for a nonlinear parabolic equation

Piotr Biler (1995)

Studia Mathematica

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The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.

On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis

Piotr Biler, Lorenzo Brandolese (2009)

Studia Mathematica

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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.

Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source

Ji Liu, Jia-Shan Zheng (2015)

Czechoslovak Mathematical Journal

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We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of...

Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth

Ning Duan, Xiaopeng Zhao (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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This paper is concerned with a fourth-order parabolic equation which models epitaxial growth of nanoscale thin films. Based on the regularity estimates for semigroups and the classical existence theorem of global attractors, we prove that the fourth order parabolic equation possesses a global attractor in a subspace of H², which attracts all the bounded sets of H² in the H²-norm.

Growth and accretion of mass in an astrophysical model, II

Piotr Biler, Tadeusz Nadzieja (1995)

Applicationes Mathematicae

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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.

Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

Yutaro Chiyo (2023)

Archivum Mathematicum

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This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version.

Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source

Yuya Tanaka (2023)

Archivum Mathematicum

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This paper deals with existence of finite-time blow-up solutions to a degenerate parabolic–elliptic Keller–Segel system with logistic source. Recently, finite-time blow-up was established for a degenerate Jäger–Luckhaus system with logistic source. However, blow-up solutions of the aforementioned system have not been obtained. The purpose of this paper is to construct blow-up solutions of a degenerate Keller–Segel system with logistic source.

Global existence versus blow up for some models of interacting particles

Piotr Biler, Lorenzo Brandolese (2006)

Colloquium Mathematicae

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We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.

The problem of data assimilation for soil water movement

François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.