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arXiv · 2601.09656

Connection of hypocoercivity and hypocontractivity via the Cayley transform

Anton Arnold·Stefan Egger·Volker Mehrmann·Eduard A. Nigsch
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Abstract

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.

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Anton Arnold, Stefan Egger, Volker Mehrmann, Eduard A. Nigsch. 2026-01-14. Connection of hypocoercivity and hypocontractivity via the Cayley transform. https://arxiv.org/abs/2601.09656

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