Hypocoercivity in Hilbert spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915127172792320 |
|---|---|
| author | Achleitner, Franz Arnold, Anton Mehrmann, Volker Nigsch, Eduard A. |
| author_facet | Achleitner, Franz Arnold, Anton Mehrmann, Volker Nigsch, Eduard A. |
| contents | The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are extended to separable Hilbert spaces. Using the concept of a hypocoercivity index, quantitative estimates on the short-time and long-time decay behavior of a hypocoercive system are derived. As a useful tool for analyzing the structural properties, an infinite-dimensional staircase form is also derived and connections to linear systems and control theory are presented. Several examples illustrate the new concepts and the results are applied to the Lorentz kinetic equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08280 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hypocoercivity in Hilbert spaces Achleitner, Franz Arnold, Anton Mehrmann, Volker Nigsch, Eduard A. Dynamical Systems 37L15, 37L05, 47D06, 35E05 The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are extended to separable Hilbert spaces. Using the concept of a hypocoercivity index, quantitative estimates on the short-time and long-time decay behavior of a hypocoercive system are derived. As a useful tool for analyzing the structural properties, an infinite-dimensional staircase form is also derived and connections to linear systems and control theory are presented. Several examples illustrate the new concepts and the results are applied to the Lorentz kinetic equation. |
| title | Hypocoercivity in Hilbert spaces |
| topic | Dynamical Systems 37L15, 37L05, 47D06, 35E05 |
| url | https://arxiv.org/abs/2307.08280 |