Asymptotic Analysis To Reaction-diffusion Systems Coupled Via Weighted Localized Sources

In this thesis, we mainly consider the reaction-diffusion systems coupled via weighted lo-calied sources, subject to homogeneous Dirichlet conditions and nonegative initial data. Weprove the global existence and non-global existence of the solutions. In particular, we give aprecise analysis on the asymptotic behavior of solutions: uniform blow-up rate and blow-up set.We give the background of the parabolic system in the introduction, and review some basicknowledge of the parabolic equation (system) in Chapter 2. In Chapter 3, we get the globalexistence and blow-up criteria for the solutions. In Chapter 4, 5 and 6, we study the singularitymore deeply to get the blow-up set and uniform blow-up rate, respectively. The blow-up setconsists of the whole domain.