Radially Symmetrical Flow of Reacting Liquid With Changing Viscosity

Frontal regimens for one-dimensional flow of reacting liquid with changing viscosity are studied. Stationary solutions are investigated for the case of narrow reaction zones that shrink to a front. The results of numerical solution of the nonstationary problem are presented. Complex oscillations resulting from period-doubling bifurcations are found

The Effect of Convection on a Propagating Front with a Liquid Product: Comparison of Theory and Experiments

This work is devoted to the investigation of propagating polymerization fronts converting a liquid monomer into a liquid polymer. We consider a simplified mathematical model which consists of the heat equation and equation for the depth of conversion for one-step chemical reaction and of the Navier-Stokes equations under the Boussinesq approximation. We fulfill the linear stability analysis of the stationary propagating front and find conditions of convective and thermal instabilities. We show that convection can occur not only for ascending fronts but also for descending fronts. Though in the latter case the exothermic chemical reaction heats the cold monomer from above, the instability appears and can be explained by the interaction of chemical reaction with hydrodynamics. Hydrodynamics changes also conditions of the thermal instability. The front propagating upwards becomes less stable than without convection, the front propagating downwards more stable. The theoretical results are compared with experiments. The experimentally measured stability boundary for polymerization of benzyl acrylate in dimethyl formamide is well approximated by the theoretical stability boundary. (C) 1998 American Institute of Physics

Fronts in subdiffusive FitzHugh–Nagumo systems

Front solutions of subdiffusive FitzHugh–Nagumo equations are studied for a piece-wise linear nonlinearity. Multiple solutions of the problem and the dependence of the propagation velocity on the parameters are discussed

Hybrid models in biomedical applications

International audienc

Mathematical Modeling of Thiol-ene Frontal Polymerization

Frontal polymerization is a method of manufacturing polymers via a self-propagating reaction wave. A mathematical model that describes thiol-ene frontal polymerization is presented and studied, both numerically and analytically. Spatio-temporal profiles of the temperature and concentrations of the reactants as well as the propagation velocity of the wave are determined. Conditions for existence of polymerization fronts are discussed. (c) 2005 Elsevier Ltd. All rights reserved

Reaction–diffusion equations in immunology

The paper is devoted to the recent works on reaction–diffusion models of virus infection dynamics in human and animal organisms. Various regimes of infection propagation in tissues are described. In particular, it is shown that infection can spread in tissues of organs as a reaction–diffusion wave. Methods for studying the conditions of the existence of wave modes of the time and space dynamics of infections is discussed. © Pleiades Publishing, Ltd., 2018

Существование решения задачи со свободной границей для систем «реакция-диффузия»

In this paper, we prove the existence of solution of a novel free boundary problem for reaction-diffusion systems describing growth of biological tissues due to cell influx and proliferation. For this aim, we transform it into a problem with fixed boundary, through a change of variables. The new problem thus obtained has space and time dependent coeffcients with nonlinear terms. We then prove the existence of solution for the corresponding linear problem, and deduce the existence of solution for the nonlinear problem using the xed point theorem. Finally, we return to the problem with free boundary to conclude the existence of its solution.В работе доказывается существование решения новой задачи со свободной границей для систем типа «реакция-диффузия», описывающих рост биологических тканей вследствие притока клеток и пролиферации. Для этого задача сводится к задаче с закрепленной границей через замену переменных. Полученная задача имеет зависящие от времени и положения в пространстве коэффициенты с нелинейными слагаемыми. Затем мы доказываем существование решения для соответствующей линейной задачи и с помощью теоремы о неподвижной точке получаем существование решения нелинейной задачи. Наконец, мы возвращаемся к задаче со свободной границей и делаем вывод о существовании ее решения