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arXiv · 2212.06092

A gradient flow for the Porous Medium Equations with Dirichlet boundary conditions

Dongkwang Kim·Dowan Koo·Geuntaek Seo
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Abstract

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.

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Dongkwang Kim, Dowan Koo, Geuntaek Seo. 2022-12-12. A gradient flow for the Porous Medium Equations with Dirichlet boundary conditions. https://arxiv.org/abs/2212.06092

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