In this work, we are concerned with generating solutions of a class Convection–Diffusion–Reaction (CDR) equation from the another CDR through Darboux transformations. The method is elucidated by cases certain types reaction coefficients. We have also discussed briefly supersymmetric pairs equations connected similarity solutions.

Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear par...

We have derived reaction-dispersal-aggregation equations from Markovian reaction-random walks with density-dependent jump rate or density-dependent dispersal kernels. From the corresponding diffusion limit we recover well-known reaction-diffusion-aggregation and reaction-diffusion-advection-aggregation equations. It is found that the ratio between the reaction and jump rates controls the onset ...

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.

• Diffusion and multi-species heterogeneous reactions in porous media are studied. Spectral approach is used to obtain new pore-scale models be homogenized. Macroscopic laws derived by homogenization technique. For high Damköhler number , complex behavior at short time successfully captured. for diffusion reversible reaction of two species developed using coupled technique spectral . Three repr...

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain ...