Critical Fujita Blow-up And Global Existence Curves For The Non-newtonian Filtration Problem In Unbounded Domains

This paper deals with a kind of non-Newtonian filtration equation with positive inner source and nonlinear boundary flux in unbounded domains.Firstly,we obtain the existence and uniqueness of local weak solutions,and then prove the comparison principle in weak sence.Next,we show the criteria of global existence and blow-up solutions.We propose the critical Fujita blow-up and global existence curves to the solutions,which depend on the degenerate terms,nonlinear sources,and the initial data.In the first chapter,we introduce the history of the corresponding problems.In the second chapter,we give the main results,which will be proved completely in the third chapter.By using the comparison principle,we obtain the global existence regions.Then by constructing the self-similar sub-solutions,we solve the Fujita blow-up exponents for the corresponding Cauchy problem.The proof of the critical Fujita blow-up curve is divided into three subcases,while the global existence curves are obtained by two subcases.