关于非Newton渗流方程的初边值问题的古典解的估计

Estimate of Classical Solutions for Non-Newton Filtration Equations with Initial or Boundary Value Problem

分别简述并证明了含有吸收项和对流项的非Newton渗流方程ut=div[(|▽u|2+ε)p2-2 ▽u]+xibi(u)+uq,(x,t)∈Bε-1×(0,T)对于边值问题:u(x,t)=0,|x|=ε-1的条件下的古典解的估计∫Bε-1ukε(x,t)dx+∫∫0tBε-1(uεk)qdxdτ≤1及初值问题:u(x,0)=kNh(kx),x∈Bε-1的条件下的古典解的估计∫0T∫Bε-1[1(+u(εk)uαεk-)1α]2|▽uεk|pdxdt≤C(α).

This paper is mainly estimate∫Bε^-1 uk^ε（x,t）dx＋∫0^t∫Bε^-1（uk^ε）^qdxdτ≤1 when boundary value problem：u（x,t）=0,│x│=ε^-1 and estimate ∫0^T∫Bε^-1（uk^ε）^α-1/[1＋（uk^ε）^α]^2│△↓uk^│^p dxdt≤C（α） when initial value problem：u（x,0）=k^Nh（kx）,x∈Bε^-1 of classical solutions u（x, y） for non-Newton filtration equations with absorption and convection：ut=div[（│△↓u│^2＋ε）^p-2/2 △↓u]δ/δxi bi（u）＋u^q（x,t）∈Bε^-1×（0,T）.