带有吸附项的边界扩散退化抛物方程解的性质

Properties of the Boundary Degenerate Parabolic Equation with Adsorption Item

研究带有吸附项的边界扩散退化抛物方程u/t=div(dα︱▽u︱p-2▽u)-uq,(x,t)∈QT=Ω×(0,T),其中:ΩRN是一个边界适当光滑的有界区域;d(x)=dist(x,Ω).验证了当α≥p-1时,该方程存在只与初值条件有关的解,而且是唯一的;当0<α<p-1时,方程存在与初值条件及边界条件有关的唯一解.

The boundary degenerate parabolic equation with adsorption item Эu/Эt=dix（d^a｜u｜^p-2u）-u^q,（x,t）∈Qr=Ω×（0,T） was studied, where OCRN was a bounded domain with appropriately smooth boundary OO,d（x） = dist（x, OO） , and it was proved that if a≥ p - 1 , the equation was admitted a unique solution subject only to a given initial datum without any boundary value condition. While if 0 〈 a 〈 p - 1 , for a given initial datum, the equation admitted different solutions for different boundary value conditions.