Perturbations and dynamics of reaction-diffusion systems with mass conservation

Stability of Stochastic Reaction-Diffusion Systems with Markovian Switching and Impulsive Perturbations

This paper is devoted to investigating mean square stability of a class of stochastic reactiondiffusion systems with Markovian switching and impulsive perturbations. Based on Lyapunov functions and stochastic analysis method, some new criteria are established. Moreover, a class of semilinear stochastic impulsive reaction-diffusion differential equations with Markovian switching is discussed and...

Large scale reaction front dynamics in anisotropic reaction-diffusion systems

Almost sure exponential stability of stochastic reaction diffusion systems with Markovian jump

The stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use Markovian jumps to model stochastic reaction diffusion systems‎. ‎In this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps‎. ‎Under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

Mass conservation and singular multicomponent diffusion algorithms

We investigate mass conservation in multicomponent diffusion algorithms. Usual diffusion matrices are indeed singular, i.e., noninvertible, because of mass conservation constraints. A consequence is that when all mass fractions are treated as independent unknowns-a widely used approach in complex chemistry reacting flow solvers-artificial singularities may appear in the governing equations. The...

Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach.

The use of reaction-diffusion models rests on the key assumption that the diffusive process is Gaussian. However, a growing number of studies have pointed out the presence of anomalous diffusion, and there is a need to understand reactive systems in the presence of this type of non-Gaussian diffusion. Here we study front dynamics in reaction-diffusion systems where anomalous diffusion is due to...