Multi-species reaction-diffusion models admitting shock solutions
نویسندگان
چکیده
A method for classifying n-species reaction-diffusion models, admitting shock solutions is presented. The most general one-dimensional twospecies reaction-diffusion model with nearest neighbor interactions admitting uniform product measures as the stationary states is studied. Satisfying more constraints, these models may experience single-shock solutions. These models are generalized to multi-species models. The two-species models are studied in detail. Dynamical phase transitions of such models are also investigated. e-mail: [email protected] e-mail: [email protected]
منابع مشابه
Multi shocks in Reaction-diffusion models
It is shown that, concerning equivalent classes, on a one-dimensional lattice with nearest neighbor interaction there are only four independent models possessing double-shocks . All these models are studied. In two of them at large times, the average width of double shock will become small, and for the other two, double shocks will be disappeared and the final state is a linear combination of B...
متن کاملTraveling Wave Solutions in Delayed Reaction Diffusion Systems with Applications to Multi-species Models
This paper is concerned with the existence of traveling wave solutions in delayed reaction diffusion systems which at least contain multi-species competition, cooperation and predator-prey models with diffusion and delays. By introducing the mixed quasimonotone condition and the exponentially mixed quasimonotone condition, we reduce the existence of traveling wave solutions to the existence of ...
متن کاملA numerical investigation of a reaction-diffusion equation arises from an ecological phenomenon
This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include ...
متن کاملOn the solvable multi–species reaction–diffusion processes
A family of one–dimensional multi–species reaction–diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the solutions to this equation, and some special solutions are given. The large–time behavior of the conditional probabilities of such systems are also investigated. ...
متن کاملAdaptive multiresolution WENO schemes for Traffic Flow Problems
Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of firstorder, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill-Whitham-Richards traffic model [4] and a model for the sedimentation of polydisperse suspensions...
متن کامل