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arXiv · 2002.11584

Anisotropic tempered diffusion equations

Juan Calvo·Antonio Marigonda·Giandomenico Orlandi
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Abstract

We introduce a functional framework which is specially suited to formulate several classes of anisotropic evolution equations of tempered diffusion type. Under an amenable set of hypothesis involving a very natural potential function, these models can be shown to belong to the entropy solution framework devised by 4, 5, therefore ensuring well-posedness. We connect the properties of this potential with those of the associated cost function, thus providing a link with optimal transport theory and a supply of new examples of relativistic cost functions. Moreover, we characterize the anisotropic spreading properties of these models and we determine the Rankine-Hugoniot conditions that rule the temporal evolution of jump hypersurfaces under the given anisotropic flows.

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Juan Calvo, Antonio Marigonda, Giandomenico Orlandi. 2020-02-26. Anisotropic tempered diffusion equations. https://doi.org/10.1016/j.na.2020.111937

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