Displaying similar documents to “Asymptotic Behavior of the Solution of the Distribution Diffusion Equation for FENE Dumbbell Polymer Model”

Exponential convergence to equilibrium Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics

Marzia Bisi, Laurent Desvillettes, Giampiero Spiga (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.


Global existence of solutions for a strongly coupled population system

Gonzalo Galiano, Ansgar Jüngel (2003)

Banach Center Publications

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A strongly coupled cross-diffusion model for two competing species in a heterogeneous environment is analyzed. We sketch the proof of an existence result for the evolution problem with non-flux boundary conditions in one space dimension, completing previous results [4]. The proof is based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional.

The quasineutral limit problem in semiconductors sciences

Ling Hsiao (2004)

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

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The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation. ...

Nonlinear evolution equations with exponential nonlinearities: conditional symmetries and exact solutions

Roman Cherniha, Oleksii Pliukhin (2011)

Banach Center Publications

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New Q-conditional symmetries for a class of reaction-diffusion-convection equations with exponential diffusivities are derived. It is shown that the known results for reaction-diffusion equations with exponential diffusivities follow as particular cases from those obtained here but not vice versa. The symmetries obtained are applied to construct exact solutions of the relevant nonlinear equations. An application of exact solutions to solving a boundary-value problem with constant Dirichlet...

Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics

Marzia Bisi, Laurent Desvillettes, Giampiero Spiga (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.

Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation

R. Rudnicki, R. Wieczorek (2010)

Mathematical Modelling of Natural Phenomena

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We present models of the dynamics of phytoplankton aggregates. We start with an individual-based model in which aggregates can grow, divide, joint and move randomly. Passing to infinity with the number of individuals, we obtain a model which describes the space-size distribution of aggregates. The density distribution function satisfies a non-linear transport equation, which contains terms responsible for the growth of phytoplankton aggregates, their fragmentation, coagulation, and...

Hypocoercive Diffusion Operators

Cédric Villani (2007)

Bollettino dell'Unione Matematica Italiana

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In many problems coming from mathematical physics, the association of a degenerate diffusion operator with a conservative operator may lead to dissipation in all variables and convergence to equilibrium. One can draw an analogy with the well-studied phenomenon of hypoellipticity in regularity theory, and actually both phenomena have been studied together. Now a distinctive theory of ``hypocoercivity'' is starting to emerge, with already some striking results, and several challenging...