Defibrillation in models of cardiac muscle.
Degenerate diffusive SEIR model with logistic population control.
Destabilization for quasivariational inequalities of reaction-diffusion type
We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
Destabilizing effect of unilateral conditions in reaction-diffusion systems
Diffusion models of multicomponent mixtures in the lung*
In this work, we are interested in two different diffusion models for multicomponent mixtures. We numerically recover experimental results underlining the inadequacy of the usual Fick diffusion model, and the importance of using the Maxwell-Stefan model in various situations. This model nonlinearly couples the mole fractions and the fluxes of each component of the mixture. We then consider a subregion of the lower part of the lung, in which we compare...
Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications
Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We propose...
Dynamic analysis of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays.
Dynamic Theory of Quasilinear Parbolic Systems. III. Global Existence.
Dynamics of Erythroid Progenitors and Erythroleukemia
The paper is devoted to mathematical modelling of erythropoiesis, production of red blood cells in the bone marrow. We discuss intra-cellular regulatory networks which determine self-renewal and differentiation of erythroid progenitors. In the case of excessive self-renewal, immature cells can fill the bone marrow resulting in the development of leukemia. We introduce a parameter characterizing the strength of mutation. Depending on its value, leukemia will or will not develop. The simplest...
Dynamics of Propagation Phenomena in Biological Pattern Formation
A large variety of complex spatio-temporal patterns emerge from the processes occurring in biological systems, one of them being the result of propagating phenomena. This wave-like structures can be modelled via reaction-diffusion equations. If a solution of a reaction-diffusion equation represents a travelling wave, the shape of the solution will be the same at all time and the speed of propagation of this shape will be a constant. Travelling wave solutions of reaction-diffusion systems have been...