la prossima settimana, per il ciclo
dei Seminari di Analisi, ci saranno due eventi:
martedì 16 aprile,
alle ore 17:00 in Aula Seminari, avremo il piacere di ascoltare Stefanos Georgiadis (KAUST), che terrà un seminario dal
titolo "Uniqueness of renormalized solutions for the Maxwell-Stefan cross-diffusion system";
giovedì 18 aprile,
alle ore 17:00 (+ merenda alle 16:45) in Aula Riunioni, avremo il piacere di ascoltare Anna Kausamo (Università degli Studi di Firenze), che terrà un seminario dal
titolo "The sufficiency of c-cyclical monotonicity for the optimality of transport plans".
Trovate qui sotto gli abstract. A
presto,
Ilaria
Lucardesi e Luigi Forcella
---------------------------------------------
Dear all,
next
week, for the Mathematical Analysis Seminar, there will be two seminars:
on Tuesday
16th April at 5PM, in "Aula Seminari", we
will have the pleasure of listening to Stefanos Georgiadis (KAUST).
The title of the talk is "Uniqueness
of renormalized solutions for the Maxwell-Stefan cross-diffusion system";
on Thursday
18th April at 5PM (+ snack at 4:45PM), in
"Aula Riunioni", we will have the pleasure of listening to Anna Kausamo (Università degli Studi di Firenze). The title of the talk is
"The sufficiency of c-cyclical monotonicity for the optimality of transport plans".
Please
find below the two abstracts. See you soon,
Ilaria
Lucardesi and Luigi Forcella
---------------------------------------------
Speaker: Stefanos
Georgiadis (KAUST)
Title: Uniqueness
of renormalized solutions for the Maxwell-Stefan cross-diffusion system
Abstract: Cross-diffusion systems are strongly coupled parabolic systems describing phenomena in which multiple species diffuse and interact with one another, e.g. in fluid
mechanics or population dynamics. Although many methods have been developed to study existence of weak solutions to such systems, uniqueness is in general an open problem. To this degree, we study a particular cross-diffusion system, known as the Maxwell-Stefan
system which describes diffusive phenomena in a multicomponent system of gases. We employ renormalized solutions and give conditions under which such solutions are unique. We, then, study the relation between weak and renormalized solutions, allowing us to
identify conditions that guarantee uniqueness of weak solutions. The proof is based on an identity for the evolution of the symmetrized relative entropy. Using the method of doubling the variables we derive the identity for two renormalized solutions and use
information on the spectrum of the Maxwell-Stefan matrix to estimate the symmetrized relative entropy and show uniqueness.
**********
Speaker: Anna Kausamo (Univ. Firenze)
Title: The sufficiency of c-cyclical monotonicity for the optimality of transport plans
Abstract: c-cyclical monotonicity is the most important
optimality condition of a transport plan. In this talk I will present a Gamma-convergence-based strategy, developed by myself and Luigi De Pascale, to prove the sufficiency of cyclical monotonicity for optimality in the multi-marginal $L^\infty$-optimal transport
case that had previously been elusive.