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arXiv · 2311.15340

Gradient Flow Solutions For Porous Medium Equations with Nonlocal L\'{e}vy-type Pressure

Guy Foghem·David Padilla-Garza·Markus Schmidtchen
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Abstract

We study a porous medium-type equation whose pressure is given by a nonlocal L\'{e}vy operator associated to a symmetric jump L\'{e}vy kernel. The class of nonlocal operators under consideration appears as a generalization of the classical fractional Laplace operator. For the class of L\'evy-operators, we construct weak solutions using a variational minimizing movement scheme. The lack of interpolation techniques is ensued by technical challenges that render our setting more challenging than the one known for fractional operators.

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Guy Foghem, David Padilla-Garza, Markus Schmidtchen. 2023-11-26. Gradient Flow Solutions For Porous Medium Equations with Nonlocal L\'{e}vy-type Pressure. https://arxiv.org/abs/2311.15340

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