Source-Type Solutions Of A Non-Newtonian Filtration Equation With Absorption And Convection

In this paper,We study the source-type solutions of the initial value problem for non-Newtonian filtration equation with absorption and convection:where p > 2, q > 0 and bi (s) ∈ C1 (R).For the case bi (u) = 0 (i.e. there is no convection term), the existence of solutins of the initial value problem (1)has been studied by Zhao Junning in [17] in 1994.The initial value problem for a Newtonian filtration equation with absorption and convection has been studied by Zhao Junning in [18] in 1995:where m ≥ 1,p > 0 and bi (s) ∈ C1 (R).Results , which we want to obtain in this paper, are correspondent to results about the non-Newtonian filtration equation with absorption in [17].In the course of proving Theorem 1 corresponding to [17] [18], we use the De Giorgi iteration, because we can't use Moser iteration like [17] [18]. This is mainly because there is not convection in [17] and the Newtonian filtration equation is studied in [18].