The Existence Of Solution Of Non-Newtonian Polytropic Filtration Equations With Sources

Non-newtonian Polytropic Filtration Equation, as a kind of important parabolic equation are derived from the spread of widespread nature phenomena. Such as Seepage theory, phase transformation theory, biological chemical and biological group dynamics, etc. Many domestic and foreign scholars have made a large amount of research for this problem in recent decades. The are a lot of significant results and important breakthrough along with studies unceasingly thorough.This article is divided into three parts. The first chapter briefly introduces physical background of non-newtonian multilateral percolation equation, as well as the research situation in the world; in the second chapter, it has discuss the main feature of solution of non-newtonian multilateral percolation equation with sources we have got the boundedness estimate and stability forλ=-1, blow-up forλ=1, and in the last of this chapter, we have study the existence of the equation range for 0<λ<1; in the third chapter it has study the existence and uniqueness of solutions of the first side value problem...