Well-Posedness For A Reaction-Diffusion Equation With Temperature In The Critical Sobolev Space

In this paper,we mainly study the well-posedness of the chemical reaction-diffusion equations with temperature in a critical Sobelev space.The reaction-diffusion equations studied in this paper describe the physical model for the change of the concentration of various substances in reversible chemical reactions of the form ?A + ?B??C.The main result is the existence and uniqueness of the small initial value solution of the reaction-diffusion equation near the equilibrium state.This article is mainly divided into the following parts:The first part is the introduction,which introduces the main background of the reaction-diffusion equation with temperature and the physical significance of the model we studied,the research progress and achievements in related fields,etc.,and then some basic knowledge and symbols used in the paper are also given.The explanation lays a theoretical foundation for the conclusions in the following paragraphs.Finally,the main results to be studied in this paper and the main ideas for proof are given.The second part is divided into two subsections,which respectively give the derivation process of the chemical reaction-diffusion system with temperature used in this paper,some basic thermodynamics and chemical knowledge used,and some lemma used in the proof of the theorem.In the third part,a rigorous proof of the existence of strong global solutions for the studied reaction-diffusion equations near the equilibrium state is given by using the energy method.First,make a small perturbation to the original equation near the equilibrium state to obtain the perturbation equation.Then,the approximation equation of the perturbation equation is constructed by iterative method,and the energy estimation of the approximation equation is given.Finally,the proof of Theorem 1.2.1is completed based on the energy estimation.