Anisotropic tempered diffusion equations
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.
Cite
@article{arxiv.2002.11584,
title = {Anisotropic tempered diffusion equations},
author = {Juan Calvo and Antonio Marigonda and Giandomenico Orlandi},
journal= {arXiv preprint arXiv:2002.11584},
year = {2020}
}
Comments
43 pages