Qualitative Research Of Solutions Of Non-newton Polytropic Filtration Equations

This paper studys mainly on non-Newton polytropic filtation equationqualitative problems. Due to non-Newton polytropic filtration equation is therepresentative to describe diffusion equation which is an important kind of partialdifferential equation. Therefore, it is attracted by mathematicians attention. In recentyears, more and more matheticians, even for physicists conducted research onnon-Newton polytropic filtration equation. Based on the theoretical results and thepractical application of the results, Newton polytropic filtration equation has notonly profound theoretical value, but also a very practical application backgroud,such as the species density, natural growth rate and so on. At the same time,non-Newton polytropic filtration equation development also expands ceaselessly,such as the solution of existence, uniqueness, regularity, progressive, the propertiesof Blow-up, the initial trace problem, the theory on interface of regularity andnonlinear source index critical index has become more perfect.This article elaborats mainly on non-Newton polytropic filtration equationsolution of qualitative research. Details are as follows:Firstly, the author conducts the research on a class of linear source non-Newtonpolytropic filtration equation weak solution. First of all, using the regularizationproblem to get the approximate solution with weak linear source non-Newtonpolytropic filtration equation and then, using the energy estimation of regularizationproblem of solution and the existence of solution to obtain the solution with weaklinear source non-Newton polytropic filtration equation.Secondly, the author studys on a class of a periodic source non Newtonpolytropic filtration equations. To get the original equations of an equivalentequation by using variable substitution, using regularized problem to get theequivalent equation approximate solution. Then, to build the existence of equivalentequationnon trivial nonnegative periodic solutions through energy estimation andLeary-Schauder theory, and then get the existence of original problem of non trivialnonnegative periodic solutions.