Related papers: Effects of Transport Memory and Nonlinear Damping …
The Fisher and Burgers' equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical…
Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized…
Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…
We present a new method to derive kinetic equations for systems undergoing non-linear transport in the presence of memory effects. In the framework of mesoscopic nonequilibrium thermodynamics, we derive a generalized Fokker-Planck equation…
Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and…
Generalizations of Onsager reciprocity relations are established for the nonlinear response coefficients of ballistic transport in the effusion of gaseous mixtures. These generalizations, which have been established on the basis of the…
An exact description of the statistical motion of active particles in three dimension is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a non-local, in time and space, connecting (memory)…
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in…
Within the real-time formulation of nonequilibrium field theory, generalized transport equations are derived avoiding the standard quasiparticle approximation. They permit to include unstable particles into the transport scheme. In order to…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
A generalized Langevin equation is suggested to describe a system with memory($u(t,t') = \frac{1}{\Gamma (\nu )}(t - t')^\nu $) as well as with positive and negative damping. The equation can be transformed into the Fokker-Planck equation…
The reaction diffusion equation arises in physical situations in problems from population growth, genetics and physical sciences. We consider the generalised Fisher equation in cylindrical coordinates from Lie theory stand point. An…
Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…
A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for…
Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for…
We study the existence of monotone heteroclinic traveling waves for a general Fisher-Burgers equation with nonlinear and possibly density-dependent diffusion. Such a model arises, for instance, in physical phenomena where a saturation…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
Strong interaction with other particles or feedback from the medium on a Brownian particle entail memory effects in the effective dynamics. We discuss the extension of the fluctuation-dissipation theorem to nonequilibrium Langevin systems…
In this work we studied a generalized Fisher equation in cylindrical coordinate using Lie symmetry method. We have determined for what type of source function the generalized Fisher equation has Lie Symmetries other than time translation…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…