The Non-Newtonian Multilateral Percolation Equation With Boundary Degeneracy

This article uses idea of partial boundary condition theory for second order linear degeneracy differential equations with nonnegative characteristic form, to carry out studying initial-boundary value problem formulation, uniqueness and existence of some nonlinear degeneracy parabolic equation.This article is divided into six parts.Chapter1briefly introduces physical background of non-Newtonian multilateral percolation equation, as well as the research situation in the world;chapter2introduces initial-boundary value problem formulation for second order (non)linear degeneracy differential equations with nonnegative characteristic form;chapter3studies double degenerate polypropic filtration equation: and gets week solution with initial value u0∈Lm+1(Ω),ρα/2▽u0m∈L∞(0, T; L2(Ω));chapter4gets the existence of W21,1week solution for some parabolic partial differential equation: Lu=aij(x,t)uxixi+bi(x,t)uxi+c(x,t)u-φt(u)=f(x,t), in(x,t)∈QT, chapter5studies and gets unique week solution for some convection diffusion equation: with initial-boundary condition under p>2,p-2/2>α>0, α≤1; chapter6studies some singular diffusion equation: and gets:(1)0<α<p-1, for any u0∈L∞(Ω) and pa|▽u0|p∈L1(Ω), there exists unique week solution of initial-boundary condition,(2) α≥p-1, dispense with boundary value, the equation admits at most one week solution with initial value.