In this paper, we prove some qualitative properties of pushed fronts for the periodic reaction-diffusion-equation with general monostable nonlinearities. Especially, exponential behavior when they are approaching their unstable state. The proof also allows us to get pulsating speed c larger than minimal speed. Through behavior, finally stability fronts.

Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary convection-diffusion equations, which are based on use of new variables. Also, we consider these equations in the form of convection-diffusion-reaction and constru...

We show that lattice dynamical systems naturally arise on infinite-dimensional invariant manifolds of reaction-diffusion equations with spatially periodic diffusive fluxes. The result connects wave pinning phenomena in lattice differential equations and in reaction-diffusion equations in inhomogeneous media. The proof is based on a careful singular perturbation analysis of the linear part, wher...

We report the study of a random Lorentz gas with a reaction of isomerization A<==>B between two colors of moving particles elastically bouncing on hard disks. The reaction occurs when the moving particles collide on catalytic disks, which constitute a fraction of all the disks. Under dilute-gas conditions, the reaction-diffusion process is ruled by two coupled Boltzmann-Lorentz equations for th...

When explicit time discretization schemes are applied to stiff reaction–diffusion equations, the stability constraint on the time step depends on two terms: the diffusion and the reaction. The part of the stability constraint due to diffusion can be totally removed if the linear diffusions are treated exactly using integration factor (IF) or exponential time differencing (ETD) methods. For syst...

We consider absorbing chemical reactions in a fluid flow modeled by the coupled advection-reaction-diffusion equations. In these systems, interplay between diffusion and transportation causes enhanced dissipation phenomenon. show that time scale, together with reaction coupling strength, determines characteristic scale of reaction.