【摘要】 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).更多还原

【Abstract】 This paper is mainly estimate ∫Bε-1uεk(x,t)dx+∫t0∫Bε-1(uεk)qdxdτ≤1 when boundary value problem:u(x,t)=0,|x|=ε-1 and estimate ∫T0∫Bε-1(uεk)α-1[1+(uεk)α]2|▽uεk|pdxdτ≤C(α) when initial value problem:u(x,0)=kNh(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-22▽u]+xibi(u)+uq,(x,t)∈Bε-1×(0,T)更多还原