Oscillatory reaction-diffusion equations with temporally varying parameters

Oscillatory Reaction-Diffusion Equations with Temporally Varying Parameters

Keywords--Reaction-diffusion, Travelling waves, A-w systems. 1. I N T R O D U C T I O N Periodic wave t ra ins are the generic one-dimensional solut ion form for react ion-diffusion equat ions with a s table l imit cycle in the kinetics. Such stable l imit cycles are used widely in biological and chemical applicat ions; chemical concent ra t ion waves such as those found wi th the BelousovZhabo...

Approximating parameters in nonlinear reaction diffusion equations ∗

We present a model describing population dynamics in an environment. The model is a nonlinear, nonlocal, reaction diffusion equation with Neumann boundary conditions. An inverse method, involving minimization of a least-squares cost functional, is developed to identify unknown model parameters. Finally, numerical results are presented which display estimates of these parameters using computatio...

Suicide substrate reaction--diffusion equations: varying the source.

The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of initial and boundary conditions are examined: one modelling an instantaneous point source, akin to an injection of substrate, the other, a continuous point source, akin to a continuing influx, or i...

Reaction-Diffusion equations with applications

Generalized reaction–diffusion equations

This Letter proposes generalized reaction–diffusion equations for treating noisy magnetic resonance images. An edge-enhancing functional is introduced for image enhancement. A number of super-diffusion operators are introduced for fast and effective smoothing. Statistical information is utilized for robust edge-stopping and diffusion-rate estimation. A quasi-interpolating wavelet algorithm is u...