Blow-up Solutions For Non-Newtonian Filtration Equations With Multi-components

This paper deals with blowup solutions also with their asymptotic properties for two classes of nonlinear parabolic equations.There are two models included: the non-Newtonian filtration equations with inner absorption coupled via nonlinear boundary flux and the parabolic equations with non-local and localized sources as well as the null Dirichlet boundary conditions.We use multiple exponents to classify the different blowup solutions with blowup rates.In Chapter 2,we deals with non-Newtonian filtration equations with inner absorption,coupled via nonlinear boundary flux.The critical global existence hyper-surface and the critical Fujita exponents which separate the region where all nontrivial solutions blow up from the one where there are both blow-up and global solutions,proved by using self-similar super-solutions and sub-solutions.At the last chapter,we consider the simultaneous and non-simultaneous blowup solutions for nonlocal nonlinear parabolic systems with variable exponents.The results are obtained with respect to the classification for the simultaneous and non-simultaneous blowup,and the corresponding blowup rates,including the phenomena: there exists only one component of the three ones blows up alone while the other two remain bounded;there exist any two of the three ones blow up simultaneously.It is interesting that the blowup property of the solutions depends on the choosing of initial data and the nonlinear inner sources of the equations.