<div class="csl-bib-body">
<div class="csl-entry">Arnold, A., Achleitner, F., Carlen, E., Nigsch, E., & Mehrmann, V. (2024, November 18). <i>Short- and long-time behavior in evolution equations: the role of the hypocoercivity index</i> [Presentation]. Partial Differential Equations Seminar 2024, Oxford, United Kingdom of Great Britain and Northern Ireland (the). http://hdl.handle.net/20.500.12708/206185</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/206185
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dc.description.abstract
The "index of hypocoercivity" is defined via a coercivity-type estimate for the self-adjoint/skew-adjoint parts of the generator, and it quantifies `how degenerate' a hypocoercive evolution equation is, both for ODEs and for evolutions equations in a Hilbert space. We show that this index characterizes the polynomial decay of the propagator norm for short time and illustrate these concepts for the Lorentz kinetic equation on a torus. Discrete time analogues of the above systems (obtained via the mid-point rule) are contractive, but typically not strictly contractive. For this setting we introduce "hypocontractivity" and an "index of hypocontractivity" and discuss their close connection to the continuous time evolution equations.
en
dc.language.iso
en
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dc.subject
Hypocoercivity
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dc.title
Short- and long-time behavior in evolution equations: the role of the hypocoercivity index
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
Rutgers, The State University of New Jersey, United States of America (the)
