Connection of hypocoercivity and hypocontractivity via the Cayley transform
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918289327783936 |
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| author | Arnold, Anton Egger, Stefan Mehrmann, Volker Nigsch, Eduard A. |
| author_facet | Arnold, Anton Egger, Stefan Mehrmann, Volker Nigsch, Eduard A. |
| contents | The concepts of hypocoercivity and hypocontractivity and their relationship are studied for semi-dissipative continuous-time and discrete-time evolution equations in a Hilbert space setting. New proofs for the characterization of the short-time decay of the solution from the initial value are presented, that in particular characterize the constants in the leading terms of the solution when expanded in time. Maximally coercive/contractive representations of hypocoercive and hypocontractive semi-dissipative systems are presented, as well as the effect of different representations on the error estimates for the numerical solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_09656 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Connection of hypocoercivity and hypocontractivity via the Cayley transform Arnold, Anton Egger, Stefan Mehrmann, Volker Nigsch, Eduard A. Dynamical Systems 37L15 (Primary) 37L05, 47D06 (Secondary) The concepts of hypocoercivity and hypocontractivity and their relationship are studied for semi-dissipative continuous-time and discrete-time evolution equations in a Hilbert space setting. New proofs for the characterization of the short-time decay of the solution from the initial value are presented, that in particular characterize the constants in the leading terms of the solution when expanded in time. Maximally coercive/contractive representations of hypocoercive and hypocontractive semi-dissipative systems are presented, as well as the effect of different representations on the error estimates for the numerical solution. |
| title | Connection of hypocoercivity and hypocontractivity via the Cayley transform |
| topic | Dynamical Systems 37L15 (Primary) 37L05, 47D06 (Secondary) |
| url | https://arxiv.org/abs/2601.09656 |