Qualitative Analysis For Two Kinds Of Reaction-diffusion Equations

In this thesis,we mainly give qualitative analysis for two kinds of reaction-diffusion equations.We will divide the thesis into five chapters.In Chapter 1, besides introducing the background and the recent advances in the two kinds of problems respectively, we will arrange the structure of this paper and state our main results.In Chapter 2, we will give the preliminary knowledge.In Chapter 3, we will deal with the blow up phenomenon of a parabolic equa-tion with weighted sources and absorption nonlinearity subject to homogeneous Dirichlet (or Neumann) boundary condition. Through constructing different aux-iliary functions, we get the lower bounds for the blowup time and blowup rate estimates for the solutions to the equation under different boundary conditions.Using the method of energy function, we obtain the upper bound for the blowup time and blowup rate estimate under the Neumann boundary condition.In Chapter 4, we will consider a kind of chemical reaction model. If the influence of the diffusion is considered, we focus on research the properties of the solution to the equations with the historical function H(u)=?u-Bu/u+1,such as stability of the equilibrium point, Turing instability and bifurcation phenomena.Chapter 5 is the last chapter of this thesis, we will summarize our results and state some open problems.