论文标题
上限和漂移变量的Hele-Shaw极限
A Hele-Shaw Limit With A Variable Upper Bound and Drift
论文作者
论文摘要
我们研究了具有源和漂移项的广义Hele-shaw方程，其中密度受到时空和时间变化的上限密度约束约束。通过使用广义的多孔培养基方程近似，我们能够在轻度假设下为广义的Hele-Shaw方程构建弱解决方案。然后，我们建立了对广义Hele-Shaw方程的弱解决方案的独特性。我们的下一个主要结果是当系统处于充血情况时，在广义的Hele-shaw方程中的密度变量的表征是一个侧面的表征。为了获得充血情况的这种表征，我们通过精制的Aronson-Benilan估计值在广义多孔培养基方程的时间衍生压力上得出了一个新的均匀下限，这意味着在密度和压力上进行单调性。
We investigate a generalized Hele-Shaw equation with a source and drift terms where the density is constrained by an upper-bound density constraint that varies in space and time. By using a generalized porous medium equation approximation, we are able to construct a weak solution to the generalized Hele-Shaw equations under mild assumptions. Then we establish uniqueness of weak solutions to the generalized Hele-Shaw equations. Our next main result is a pointwise characterization of the density variable in the generalized Hele-Shaw equations when the system is in the congestion case. To obtain such a characterization for the congestion case, we derive a new uniform lower bounds on the time derivative pressure of the generalized porous medium equation via a refined Aronson-Benilan estimate that implies monotonicity on the density and pressure.
