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

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arxiv 2212.06092 v3 pith:7KMKK7N7 submitted 2022-12-12 math.AP math.OC

Dongkwang Kim , Dowan Koo , Geuntaek Seo This is my paper · ORCID
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keywords equationsboundaryconditionsdirichletdistanceflowgradientmedium
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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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  1. Sharp Continuity Moduli for Dirichlet Heat Flow in Boundary-Reservoir Transport Metrics

    math.AP 2026-07 conditional novelty 6.0 of 10

    The killed Dirichlet heat semigroup is Lipschitz in W_{b,1}, exactly 1/p-Hölder on mass sublevels in W_{b,p} for p>1, and discontinuous at zero, which obstructs EVI_λ realizations in W_{b,2}.

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