边界退化的对流扩散方程

Diffusion Convection Equation with Boundary Degeneracy

考虑对流扩散方程:Nbui(u)t=div(ρα|▽u| p-2▽u)+∑Ni=bi(u)/xi,(x,t)∈QT=Ω×(0,T)其中对流项∑Ni=bi(u)/xi满足bi(s)≤c|s|1+β,b′i(s)≤c|s|β.利用抛物正则化方法讨论该对流方程初边值问题解的定义,并在(p-2)/2>α>1下证明该问题存在唯一的弱解.

The diffusion convection equation with boundary degeneracy Nbui（u）t=div（ρα｜▽u｜ p-2▽u）＋∑Ni=bi（u）/xi,（x,t）∈QT=Ω×（0,T）was researched by the parabolic regularization method,where the convective term ∑Ni=bi（u）/xi satisfies bi（s）≤c｜s｜1＋β,b′i（s）≤c｜s｜β.We also studied how to quote the initial boundary value problem,and proved the existence and the uniqueness of the solutions under some additional conditions such as（p-2）/2〉α〉1.