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A nonlocal coagulation-fragmentation model

Mirosław Lachowicz, Dariusz Wrzosek (2000)

Applicationes Mathematicae

A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local...

Classification des solutions d’un problème elliptique fortement non linéaire

A. Benaouda, A. Gmira, B. Hamri (2005)

Annales mathématiques Blaise Pascal

On étudie la classification des solutions du problème elliptique ( u ′ p - 2 u ′ ) ′ ( t ) + u q - 1 u ′ ( t ) - f ( t ) u m - 1 u ( t ) = 0 , t > 0 , où q > 1 , p ≥ m + 1 > 2 et f une fonction changeant de signe. En utilisant une méthode de tire, On montre qu’en partant avec une dérivée initiale nulle toutes les solutions sont globales. De plus si p > m + 1 et q > ( p - 1 ) ( m + 1 ) / p l’ensemble des solutions est constitué d’une seule solution à support compact et de deux familles de solutions ; celles qui sont strictement positives et celles qui changent de signes. On montre aussi que ces deux familles tendent vers l’infini quand...

Coupling of chemical reaction with flow and molecular transport

Ulrich Maas (1995)

Applications of Mathematics

During the last years the interest in the numerical simulation of reacting flows has grown considerably. Numerical methods are available, which allow to couple chemical kinetics with flow and molecular transport. However, the use of detailed physical and chemical models, involving more than 100 chemical species, and thus more than 100 species conservation equations, is restricted to very simple flow configurations like one-dimensional systems or two-dimensional systems with very simple geometries,...

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

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.

Exponential convergence to equilibrium via 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


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.


Fluid-dynamic equations for reacting gas mixtures

Marzia Bisi, Maria Groppi, Giampiero Spiga (2005)

Applications of Mathematics

Starting from the Grad 13-moment equations for a bimolecular chemical reaction, Navier-Stokes-type equations are derived by asymptotic procedure in the limit of small mean paths. Two physical situations of slow and fast reactions, with their different hydrodynamic variables and conservation equations, are considered separately, yielding different limiting results.

Isomerism as Manifestation of Intrinsic Symmetry of Molecules: Lunn–Senior’s Theory

Iliev, Valentin (2009)

Serdica Journal of Computing

This article presents the principal results of the doctoral thesis “Isomerism as internal symmetry of molecules” by Valentin Vankov Iliev (Institute of Mathematics and Informatics), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 15 December, 2008.This paper is an extended review of our doctoral thesis “Isomerism as Intrinsic Symmetry of Molecules” in which we present, continue, generalize, and trace out Lunn–Senior’s theory of isomerism...

Kinetical systems

Ladislav Adamec (1997)

Applications of Mathematics

The aim of the paper is to give some preliminary information concerning a class of nonlinear differential equations often used in physical chemistry and biology. Such systems are often very large and it is well known that where studying properties of such systems difficulties rapidly increase with their dimension. One way how to get over the difficulties is to use special forms of such systems.

On aliases of differential equations

Rutherford Aris, Gianni Astarita (1989)

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

Theory of chemical reactions in complex mixtures exhibits the following problem. Single reacting species follow an intrinsic kinetic law. However, the observable quantity, which is a mean of individual concentrations, follows a different law. This one is called «alias» of intrinsic kinetics. In this paper the phenomenon of alias of uniform families of differential equations is discussed in general terms.

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