Séminaire d'analyse
On the Entropy Production OperatorVincent Perrollaz (IDP Tours)
Thursday 09 October 2025 14:00 - Tours - E2290
Résumé :
Kruzkov entropies single out the “good” solution among all weak solutions to a general scalar balance law. This is coherent with the selection based on any other convex entropy E.
We provide an explicit and quantitative formula expressing the E entropy production in term of the Kruzkov entropy production. Indeed this representation applies to any bounded function not necessarily related to the balance law.
This motivates the introduction of a general entropy production operator and the analysis of its functional properties. Topological considerations constrain the framework to the projective tensor product of C^1 spaces for fluxes, entropies and entropy fluxes. Surprisingly, complex valued entropies and Fourier transform techniques provide families of entropies, alternative to the Kruzkov one, still able to characterize this operator. As a byproduct, this general approach also shows that the entropy production furnishes a faithful representation of any essentially bounded function.
This talk is based on joint works with Rinaldo M. Colombo.
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