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Quasichemical Models of Multicomponent Nonlinear Diffusion

A.N. Gorban, H.P. Sargsyan, H.A. Wahab (2011)

Mathematical Modelling of Natural Phenomena

Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special tools are needed to provide the systematic construction of the nonlinear diffusion equations for multicomponent mixtures with significant interaction between components. We develop an approach to nonlinear multicomponent...

Regularity and approximability of the solutions to the chemical master equation

Ludwig Gauckler, Harry Yserentant (2014)

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

The chemical master equation is a fundamental equation in chemical kinetics. It underlies the classical reaction-rate equations and takes stochastic effects into account. In this paper we give a simple argument showing that the solutions of a large class of chemical master equations are bounded in weighted ℓ1-spaces and possess high-order moments. This class includes all equations in which no reactions between two or more already present molecules and further external reactants occur that add mass...

Stability of a model for the Belousov-Zhabotinskij reaction

Vladimír Haluška (1989)

Aplikace matematiky

The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.

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