<div class="csl-bib-body">
<div class="csl-entry">Arnold, A. (2024, September 9). <i>All relative entropies for general nonlinear Fokker-Planck equations</i> [Conference Presentation]. 12th Edition of Particle Systems and PDE’s (PSPDE XII), Triest, Italy.</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/200684
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dc.description.abstract
We shall revisit the entropy method for quasilinear Fokker-Planck equations with confinement to deduce exponential convergence to the equilibrium. Even for prototypical examples like the porous-medium equation, only one relative entropy has been known so far - the Ralston-Newman entropy, which is the analog of the logarithmic entropy in the linear case. We shall give a complete characterization of all admissible relative entropies for each quasilinear Fokker-Planck equation. In particular we find that fast-diffusion equations with power-law nonlinearities admit only one entropy, while porous medium equations give rise to a whole family of admissible relative entropies (similar to linear Fokker-Planck equations). These additional entropies then imply also new moment-control estimates on the porous-medium solution. Joint work with Jose Carrillo, Daniel Matthes.
en
dc.language.iso
en
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dc.subject
entropy method
en
dc.title
All relative entropies for general nonlinear Fokker-Planck equations
