Displaying similar documents to “Stationary solutions of aerotaxis equations”

A model of evolution of temperature and density of ions in an electrolyte

Andrzej Raczyński (2005)

Applicationes Mathematicae

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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.

On stationary kinetic systems of Boltzmann type and their fluid limits

Leif Arkeryd (2004)

Banach Center Publications

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The first part reviews some recent ideas and L¹-existence results for non-linear stationary equations of Boltzmann type in a bounded domain in ℝⁿ and far from global Maxwellian equilibrium. That is an area not covered by the DiPerna and P. L. Lions methods for the time-dependent Boltzmann equation from the late 1980-ies. The final part discusses the more classical perturbative case close to global equilibrium and corresponding small mean free path limits of fully non-linear stationary...

Stationary reflection in extender models

Ernest Schimmerling (2005)

Fundamenta Mathematicae

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Working in L[E], we examine which large cardinal properties of κ imply that all stationary subsets of cof(<κ) ∩ κ⁺ reflect.

Unique global solvability of 1D Fried-Gurtin model

Zenon Kosowski (2007)

Applicationes Mathematicae

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We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified...

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

Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja (1994)

Colloquium Mathematicae

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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.

Stationary states and moving planes

Gerhard Ströhmer (2008)

Banach Center Publications

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Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.

Molecular motors and stochastic networks

Reinhard Lipowsky, Steffen Liepelt (2008)

Banach Center Publications

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Molecular motors are nano- or colloidal machines that keep the living cell in a highly ordered, stationary state far from equilibrium. This self-organized order is sustained by the energy transduction of the motors, which couple exergonic or 'downhill' processes to endergonic or 'uphill' processes. A particularly interesting case is provided by the chemomechanical coupling of cytoskeletal motors which use the chemical energy released during ATP hydrolysis in order to generate mechanical...

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.

Chemotaxis models with a threshold cell density

Dariusz Wrzosek (2008)

Banach Center Publications

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We consider a quasilinear parabolic system which has the structure of Patlak-Keller-Segel model of chemotaxis and contains a class of models with degenerate diffusion. A cell population is described in terms of volume fraction or density. In the latter case, it is assumed that there is a threshold value which the density of cells cannot exceed. Existence and uniqueness of solutions to the corresponding initial-boundary value problem and existence of space inhomogeneous stationary solutions...

Modeling Non-Stationary Processes of Diffusion of Solute Substances in the Near-Bottom Layer ofWater Reservoirs: Variation of the Direction of Flows and Assessment of Admissible Biogenic Load

V. V. Kozlov (2009)

Mathematical Modelling of Natural Phenomena

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The paper is devoted to mathematical modelling and numerical computations of a nonstationary free boundary problem. The model is based on processes of molecular diffusion of some products of chemical decomposition of a solid organic substance concentrated in bottom sediments. It takes into account non-stationary multi-component and multi-stage chemical decomposition of organic substances and the processes of sorption desorption under aerobic and anaerobic conditions. Such a model allows...