论文标题
多孔介质方程的自由边界规律性，非本地漂移在维度
Free Boundary Regularity of the Porous Medium Equation with nonlocal drifts in Dimension One
论文作者
论文摘要
我们研究了多孔培养基方程的自由边界，其中非局部漂移在维度为一。在假设初始数据在自由边界处具有超季度增长的假设，我们表明该解决方案在空间中是平滑的，$ c^{2,1} _ {\ loc} $的时间是及时的，然后自由边界为$ c^{2,1} _ {\ loc} $。此外，如果漂移是局部的，则解决方案和自由边界都是光滑的。
We study the free boundary of the porous medium equation with nonlocal drifts in dimension one. Under the assumption that the initial data has super-quadratic growth at the free boundary, we show that the solution is smooth in space and $C^{2,1}_{\loc}$ in time, and then the free boundary is $C^{2,1}_{\loc}$. Moreover if the drift is local, both the solution and the free boundary are smooth.
