中文摘要：

考虑带对流项的多孔介质方程：ut=div（ρ^α▽um）＋i=1∑N bi（u^m）/xi,（x,t）∈QT=Ω×（0,T）.假设对任意的i∈{1,2,…,N},bi（s）是C1函数,且存在常数β,c,使得bi（s）≤c｜s｜^1＋β,｜b′i（s）｜≤c｜s｜^β.应用抛物正则化方法,得到了该方程在条件0〈α〈1时初边值问题解的存在唯一性.

英文摘要：

The authors studied diffusion convection equation with boundary degeneracy ut=div（ρ^α▽um）＋i=1∑N bi（u^m）/xi,（x,t）∈QT=Ω×（0,T）.,for any i∈{1,2,…,N},b i（s）is a C1 function,there are constantsβ,c such that bi（s）≤c｜s｜^1＋β,｜b′i（s）｜≤c｜s｜^β.If 0〈α〈1,the existence and the uniqueness of the solutions of the initial-boundary value problem to the equation were obtained by the parabolic regularized method.