ÖMG Tagung 2023 : Meeting of the Austrian Mathematical Society
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Event date:
18-Sep-2023 - 22-Sep-2023
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Event place:
Graz, Austria
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Number of Pages:
1
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Keywords:
hypocoercivity (index); dissipative system; evolution equation; decay rate; staircase form
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Abstract:
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. The results are applied to the Lorentz kinetic equation.
