The Qualitative Research Of Reaction-diffusion System With Depositings

Diffusion phenomenon is very common in nature. We can describe of partialdifferential equations with diffusion to reveal internal movement rules of thisnatural phenomenon. Reaction-diffusion equation is formed by adding reactionterm and widely applied in areas such as population dynamics.This paper studies is a kind of reaction-diffusion system with depositings,which is a kind of reaction-diffusion equations with initial boundary value. Thereis strict physical significance in coefficient of reaction-diffusion equations. Thesolution to reaction-diffusion system reflect two biological populations’ quantitychange in limited region. This author establishes a new approximate system byweakening the solution to reaction-diffusion system. Then he makes a series ofconsensus estimates of the solution to approximate system and gets the sufficientconditions of the existence of solution in original system.Firstly, the author introduces the history development of partial differentialequations, the development process of reaction-diffusion equations and severalcommon research direction of reaction-diffusion equations; Secondly, heintroduces preparation knowledge, including three commonly used importantinequation, Sobolev embedded theorem and De Giorgi iterativetechnology.Furthermore, the author uses inequality and embedded theorem tosolve actual examples and iterative technology to estimate the maximummodulus of a specific nonhomogeneous heat equation by De Giorgi terativetechnology; Thirdly, the author gives definition weak solution because theresearch system may not have the classical solution, and regularizes the originalsystem in chapter3. Through researching the new solution to approximate system,he gains three important lemma and the proof of the solution existence; Finally,the author summarizes the main results, points out the deficiency and futureresearch direction in the last paper part.