Mathematical analysis of non linear reaction diffusion process in chemical sciences

Abstract

Reaction-diffusion describes the process in which multiple newlineparticipating chemicals or agents react with each other, while simultaneously newlinediffusing or spreading through a liquid or gaseous medium. Typically, these newlineprocesses are studied for their ability to produce nontrivial patterns that evolve newlineover time. These patterns, often referred to as Turing structures or Turing newlinepatterns, are diffusion driven. In the presence of diffusion, the Turing patterns newlineare observable, but are not present in the absence of diffusion. It is important for newlinereaction diffusion models to replicate the behavior that is experimentally newlineobserved. That is to say that the models must be able to produce solutions with newlinetraits, such as pattern type, that are similar to experimentally observed traits. newlineMathematically, we seek to explain certain aspects of the models such as pattern newlineselection in the hope of broadening our understanding of the underlying process newlinefor which the model represents. newlineNon- linear reaction diffusion systems are mathematical models newlinewhich correspond to several physical phenomena. The most common is the newlinechange in space and time of the concentration of one or more chemical newlinesubstances: local chemical reactions in which the substances are transformed newlineinto each other, and diffusion which causes the substances to spread out over a newlinesurface in space. newlineReaction diffusion systems are naturally applied in chemistry. newlineHowever, the system can also describe dynamical processes of non-chemical newlinenature. newline