奇异半线性反应扩散方程组Cauchy问题

本文讨论如下问题其中σ>0,Pi>1,qi>1(i=1,2),α1≥0,α2>0,β1>0,β2≥0,fi(x)(i=1,2)连续有界非负, (f1(x),f2(x))(?)(0,0).给出了非负局部解存在的几个充分条件和解的爆破结果.     

A free boundary problem describing reaction-diffusion problems in chemical vapor infiltration of pyrolytic carbon

In this paper we consider chemical vapor deposition of pyrolytic carbon from methane in hot wall reactors. Especially, we deal with the interaction of homogeneous gas-phase and heterogeneous surface reactions. The resulting mathematical model is composed of a system of reaction-diffusion equations in a corner domain supplied with the Gibbs-Thomson law, which describes the movement of the free boundary, arising from the carbon deposition. We prove a short time existence and uniqueness result in Hölder spaces. We achieve this by contraction arguments and transforming the Gibbs-Thomson law to local coordinates to obtain a nonlinear parabolic equation on a manifold.     

The poisson representation. II Two-time correlation functions

Basic formulas for the two-time correlation functions are derived using the Poisson representation method. The formulas for the chemical system in thermodynamic equilibrium are shown to relate directly to the fluctuationdissipation theorems, which may be derived from equilibrium statistical mechanical considerations. For nonequilibrium systems, the formulas are shown to be generalizations of these fluctuation-dissipation theorems, but containing an extra term which arises entirely from the nonequilibrium nature of the system. These formulas are applied to two representative examples of equilibrium reactions (without spatial diffusion) and to a nonequilibrium chemical reaction model (including the process of spatial diffusion) for which the first two terms in a systematic expansion for the two-time correlation functions are calculated. The relation between the Poisson representation method and Glauber-SudarshanP-representation used in quantum optics is discussed.     

TARGET PATTERNS AND SPIRAL WAVES IN REACTION-DIFFUSION SYSTEMS WITH LIMIT CYCLE KINETICSAND WEAK DIFFUSION

1.IntroductionTargetpatternsandspiralwavesarecommonlyobservedincertainmodelsofchemicalandbiologicalsystemssuchastheBelousov-ZhabotinskiireactionandthesocialamoebasDictyosteliumdiscoideium(of.11--4]andthereferencestherein).Thesesystemsaregovernedbyachemicalorbiologicalreactionandspatialdiffusion,i.e.reaction-diffusionequations.Generallyspeaking,atargetpatternisasetofconcentricringsofconstantconcentrationeachmovingoutward.Alonganyradialline,thepatternbehavesasymptoticallylikeaperiodictravellin…     

Computational Modelling of Biosensors with Perforated and Selective Membranes

This paper presents a two-dimensional-in-space mathematical model of amperometric biosensors with perforated and selective membranes. The model is based on the diffusion equations containing a non-linear term of the Michaelis–Menten enzymatic reaction. Using numerical simulation of the biosensors action, the influence of the geometry of the perforated membrane on the biosensor response was investigated. The numerical simulation was carried out using finite-difference technique. The calculations demonstrated non-linear and non-monotonous change of the biosensor steady-state current at various degree of the surface of the perforated membrane covering. The non-monotonous behaviour of the biosensor response was also observed when changing the thickness of the perforated membrane.     

Modeling of electrocatalytic processes at conducting polymer modified electrodes

A mathematical model of electrocatalytic processes taking place at conducting polymer modified electrodes has been developed. The model takes into account the diffusion of solution species into a polymer film, diffusion of charge carriers within the film, and a chemical redox reaction within the film. The space- and time-resolved profiles for reactant and charge carrier concentration within the film, as well as dependencies of electric current on the concentration of solute species, reaction rate constant and thickness of a polymer layer have been obtained and discussed. It has been shown that, even at a relatively fast diffusion of charge carriers within the conducting polymer film, exceeding the diffusion rate of reactant by two orders of magnitude, electrocatalysis of solute species at conducting polymer modified electrodes proceeds within the polymer film rather than at the outer polymer/solution interface, i.e., electrocatalytic conversion follows a redox-mechanism rather than metal-like one. Based on the results obtained, optimization of reaction system parameters could be made for any particular case to get an optimum efficiency or reactant to product conversion.      

Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input

We investigate with the help of analytical and numerical methods the reactionA+AA on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for largex, the particle concentrationc(x) behaves likeA _s x ^–1 (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opposite direction, the particle concentration behaves likeA _a x ^–1/2. The constantsA _s andA _a are independent of the input and the two coagulation rates. The universality ofA _a comes as a surprise, since in the asymmetric case the system has a massive spectrum.     

Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities

Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.     

一类具有分布时滞和非局部空间效应的合作模型的稳定性

构造并研究了一类具有分布时滞和非局部空间效应影响的两种群成年个体相互合作的反应扩散模型.利用线性稳定化方法和Redlinger上下解方法得到了该合作模型的动力性态,并证明了模型在零平衡点和边界平衡点是不稳定的,而在正平衡点是全局渐近稳定的.     

ASYMPTOTICAL ANALYSIS OF A REACTIONDIFFUSION EQUATIONS D-SIS EPIDEMIC MODEL

By monotone methods and invariant region theory,a reaction-diffusion equa- tions D-SIS epidemic model with bilinear rate is studied.The existence and uniqueness of the solution of the model are proved.The basic reproductive number which determines whether the disease is extinct or not is found.The globally asymptotical stability of the disease-free equilibrium and the endemic equilibrium are obtained.Some results of the ordinary differential equations model are extended to the present partial differential equations model.