Displaying similar documents to “Generalized kinetic equations and effective thermodynamics”

On the unique solvability of a nonlocal phase separation problem for multicomponent systems

Jens A. Griepentrog (2004)

Banach Center Publications

Similarity:

A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction...

Nonisothermal systems of self-attracting Fermi-Dirac particles

Piotr Biler, Tadeusz Nadzieja, Robert Stańczy (2004)

Banach Center Publications

Similarity:

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.

Asymptotic self-similar blow-up for a model of aggregation

Ignacio Guerra (2004)

Banach Center Publications

Similarity:

In this article we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see e.g. M. P. Brenner et al. 1999, Nonlinearity 12, 1071-1098); one type is self-similar, and may be viewed as a trade-off between...

Growth and accretion of mass in an astrophysical model, II

Piotr Biler, Tadeusz Nadzieja (1995)

Applicationes Mathematicae

Similarity:

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.

Blow-up of a nonlocal p-Laplacian evolution equation with critical initial energy

Yang Liu, Pengju Lv, Chaojiu Da (2016)

Annales Polonici Mathematici

Similarity:

This paper is concerned with the initial boundary value problem for a nonlocal p-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.

Global existence versus blow up for some models of interacting particles

Piotr Biler, Lorenzo Brandolese (2006)

Colloquium Mathematicae

Similarity:

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.

A stochastic phase-field model determined from molecular dynamics

Erik von Schwerin, Anders Szepessy (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation...

Kinetic and hydrodynamic equations for granular media

Mario Pulvirenti (1999)

Journées équations aux dérivées partielles

Similarity:

In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.

Blow-up versus global existence of solutions to aggregation equations

Grzegorz Karch, Kanako Suzuki (2011)

Applicationes Mathematicae

Similarity:

A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.

Evolution equations in non-cylindrical domains

Piermarco Cannarsa, Giuseppe Da Prato, Jean-Paul Zolésio (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

We develolp a new method to solve an evolution equation in a non-cylindrical domain, by reduction to an abstract evolution equation..

Computer simulation of the atomic behaviour in condensed phases.

Antoni Giró Roca, Joan Angel Padró (1987)

Qüestiió

Similarity:

Molecular dynamics simulation method for the study of condensed phases of matter is described in this paper. Computer programs for the simulation of atomic motion have been developed. Time-saving techniques, like the cellular method have been incorporated in order to optimize the available computer resources. We have applied this method to the simulation of Argon near its melting point. Differences in the structure, thermodynamic properties and time correlation functions of solid and...