Related papers: On reaction-subdiffusion equations
We present a general method to produce well-conditioned continuum reaction-drift-diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e.,…
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $\lambda$--$\newrho$ model for irreversible…
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as…
The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. Such problems describe biological processes and chemical reactions in which diffusive and…
In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on…
We give an explicit formula for the change of speed of pushed and bistable fronts of the reaction diffusion equation when a small cutoff is applied at the unstable or metastable equilibrium point. The results are valid for arbitrary…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…
In this paper, we extend some of the multilevel convergence results obtained by Xu and Zhu in [Xu and Zhu, M3AS 2008], to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions can be written as a euclideen Schr\"odinger equation in which the wave function is the probability distribution and the Hamiltonian is…
We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…
We consider the trapping reaction A + B -> B in space dimension d<=2. By formally eliminating the B particles from the problem we derive an effective dynamics for the A particles from which the survival probability of a given A particle and…
In this paper we study the asymptotic nonlinear dynamics of scalar semilinear parabolic problems reaction-diffusion type when the diffusion coefficient becomes large in a subregion which is interior to the domain. We obtain, under suitable…
We show an application of a subdiffusion equation with Caputo fractional time derivative with respect to another function $g$ to describe subdiffusion in a medium having a structure evolving over time. In this case a continuous transition…
Chemical reactions are a prominent feature of molecular communication (MC) systems, with no direct parallels in wireless communications. While chemical reactions may be used inside the transmitter nodes, receiver nodes or the communication…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…
A complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It is shown that all the known results for reaction-diffusion equations with power…