Suicide substrate reaction-diffusion equations: Varying the source

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...

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...

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...

Reaction-diffusion Equations

I have recently worked in the area of partial differential equations (PDE), specifically reaction-diffusion equations, drift-diffusion equations, and fluid dynamics. These equations model physical processes such as combustion, mixing, or turbulence, and my main interest has been in long term dynamics of their solutions as well as in the formation of singularities. I consider myself an applied a...

Reaction-Diffusion Equations and Learning