PreprintCC BY 4.0HAL
Fractional hypocoercivity in bounded domains in the anomalous diffusion limit
Abstract
In this paper, we provide quantitative stability results for several dissipative linear kinetic equations with heavy-tailed equilibria in different geometries. Moreover, the approach, inspired by the so-called L2-hypocoercivity method, is robust enough to provide estimates that are uniform in the anomalous diffusion limit. It applies to bounded domains with either periodic or general Maxwell boundary conditions (ranging from the pure specular to the pure diffusive case) as well as to the whole-space case. In addition, our framework accommodates linear collisional operators whose coefficients depend on the position.
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BibTeX
@misc{herda2026fractional,
title = {{Fractional hypocoercivity in bounded domains in the anomalous diffusion limit}},
author = {Maxime Herda and Marc Pegon and Isabelle Tristani},
howpublished = {HAL},
year = {2026},
month = oct,
eprint = {2512.20222},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05430140v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fractional hypocoercivity in bounded domains in the anomalous diffusion limit
AU - Maxime Herda
AU - Marc Pegon
AU - Isabelle Tristani
PY - 2026
DA - 2026/10/14
PB - HAL
UR - https://hal.science/hal-05430140v2
AB - In this paper, we provide quantitative stability results for several dissipative linear kinetic equations with heavy-tailed equilibria in different geometries. Moreover, the approach, inspired by the so-called L^2-hypocoercivity method, is robust enough to provide estimates that are uniform in the anomalous diffusion limit. It applies to bounded domains with either periodic or general Maxwell boundary conditions (ranging from the pure specular to the pure diffusive case) as well as to the whole-space case. In addition, our framework accommodates linear collisional operators whose coefficients depend on the position.
ER -