论文标题
具有Dirichlet边界条件的多孔介质方程的梯度流量
A gradient flow for the Porous Medium Equations with Dirichlet boundary conditions
论文作者
论文摘要
我们考虑具有非阴性恒定dirichlet边界条件的多孔介质方程的梯度流结构。我们通过最小化移动方案来构建方程较弱的解决方案，通过考虑相对于$ WB_2 $距离的熵功能，这是Figalli和Gigli引入的修改的Wasserstein距离[J。数学。 Pures Appl。 94，（2010），第107-130页]。此外，构造的解决方案在适当的意义上被视为最大斜率的曲线。
We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy functional with respect to $Wb_2$ distance, which is a modified Wasserstein distance introduced by Figalli and Gigli [J. Math. Pures Appl. 94, (2010), pp. 107-130]. Furthermore, the constructed solutions are characterized as curves of maximal slope in a suitable sense.
