On Some Properties Of Solutions To Several Types Of Nonlinear Parabolic Systems

The rapid development of the theory of partial di?erential equationsand the prolific growth of its applications have made it importance for usto study the basic theory of parabolic equations (systems). The propertiesof solutions to the four types of nonlinear parabolic equations (systems)have been studied in this dissertation, such as, support properties, uniformboundedness, global existence, finite-time blowup, and blow-up rate, etc.The thesis consists of five chapters. The first chapter is devote to thesummary of the dissertation, which recounts the background, the devel-opment, and the present circumstance about related problems. Moreover,main results of the present paper are stated.In chapter 2, we study the support properties of solutions to theCauchy problem on the following equation:ρ(|x|)ut = div(um?1|Du|λ?1Du)?f(u). We deal with localization property and asymptotic behavior of solu-tions to this type of equation in several dimensional spaces. On the otherhand, we study the appearance of interfaces in one dimensional space.In chapter 3, we investigate the uniform boundedness of global so-lutions to the equation with general structure localization reaction:ut =?u + f(u(x0(t),t)). We consider the problem in two cases: fixed sourceand moving source. For the former, we show that all global solutions areuniformly bounded in dimension n; for the latter, we also prove the corre-sponding conclusion holds in dimension 1.In chapter 4, we consider the blow-up properties of the solution to thefollowing parabolic system with localization reaction : ut = ?u + up1(x0,t)...