October 2022 - Analysis-seminar - Mailing list — Dipartimento di Matematica, UniPI

[Indico] Prof. Idriss Mazari, Existence of optimal shapes in optimal control theory, 10/18/22, 5:00 PM Europe/Rome
by maria.stella.gelli＠unipi.it 18 Oct '22

18 Oct '22

Title: Existence of optimal shapes in optimal control theory, Speaker(s): Prof. Idriss Mazari, Université de Paris Dauphine, Date and time: Oct 18, 2022, 5:00 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/119 -- Indico :: Email Notifier https://events.dm.unipi.it/e/119

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[Indico] Prof. Idriss Mazary, Existence of optimal shapes in optimal control theory, 18/10/2022, 17:00 Europe/Rome
by maria.stella.gelli＠unipi.it 13 Oct '22

13 Oct '22

Title: Existence of optimal shapes in optimal control theory, Speaker(s): Prof. Idriss Mazary, Université de Paris Dauphine, Date and time: 18 Oct 2022, 17:00 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Riunioni). You can access the full event here: https://events.dm.unipi.it/e/119 -- Indico :: Email Notifier https://events.dm.unipi.it/e/119

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[Indico] Prof. Idriss Mazary, Existence of optimal shapes in optimal control theory, 10/18/22, 5:00 PM Europe/Rome
by maria.stella.gelli＠unipi.it 11 Oct '22

11 Oct '22

Title: Existence of optimal shapes in optimal control theory, Speaker(s): Prof. Idriss Mazary, Université de Paris Dauphine, Date and time: Oct 18, 2022, 5:00 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Seminari). You can access the full event here: https://events.dm.unipi.it/e/119 Abstract -------- In this talk, we present several recent contributions (in collaboration with G. Nadin and Y. Privat) on the question of the existence of optimal shapes in optimal control theory for bilinear models. Motivated by applications in spatial ecology, we investigate the following problem: consider a parabolic or elliptic equation$Lu=mu+F(u)$ where $L$ is a parabolic or elliptic operator, $m$ is the control and $F$ is a given non-linearity. The goal is to solve the optimisation problem$$Max_m \int_\Omega j(x;u)\,dx$$where $j$ is simply a cost functional, and $m$ is an admissible control that satisfies $L^1$ and $L^\infty$ bounds. In other words, we assume $0\le m\le1$ almost everywhere, and $\int_\Omega m\,dx=V_0$ where $V_0$ is a fixed volume constraint. A basic property for such problem is to obtain the bang-bang property for maximisers. In other words, are optimal control characteristic functions of subsets of the domain on which the equation is set? Put otherwise, can optimisers be identified with subsets of the domain? What we explain in this talk is that for bilinear control problems, the answer is analogous to the Buttazzo-DalMaso theorem: if the functional we want to optimise is monotonic, then the answer to this question is positive. Our result relies on new oscillatory techniques. Note ---- Il seminario di martedi' 18 ottobre si terrà in sala Riunioni invece che in Sala Seminari a causa della concomitanza con un Meeting Erasmus già programmato in Sala Seminari -- Indico :: Email Notifier https://events.dm.unipi.it/e/119

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[Indico] Gaetano Siciliano, Critical points at prescribed energy levels, 10/10/22, 5:00 PM Europe/Rome
by maria.stella.gelli＠unipi.it 10 Oct '22

10 Oct '22

Title: Critical points at prescribed energy levels, Speaker(s): Gaetano Siciliano, Univ. San Paulo, Br, Date and time: Oct 10, 2022, 5:00 PM (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Sala Seminari). You can access the full event here: https://events.dm.unipi.it/e/121 Abstract -------- In this talk, we discuss the existence of critical points for a family of abstract and smooth functionals on Banach spaces under the energy constraint. By using the Ljusternick-Schnirelmann theory and the fibering method of Pohozaev we show, under suitable assumptions, multiplicity results.The abstract framework is then applied to some partial differential equations depending on a parameter for which we obtain multiple solutions as well as some bifurcation results. -- Indico :: Email Notifier https://events.dm.unipi.it/e/121

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[Indico] Elia Bruè, Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, 28/06/2022, 16:30 Europe/Rome
by maria.stella.gelli＠unipi.it 03 Oct '22

03 Oct '22

Title: Non-uniqueness of Leray solutions of the forced Navier-Stokes equations, Speaker(s): Elia Bruè, Institute for Advanced Study (Princeton), Date and time: 28 Jun 2022, 16:30 (Europe/Rome), Lecture series: Analysis Seminar, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/100 Abstract -------- In his seminal work, Leray demonstrated the existence of global weak solutions, with nonincreasing energy, to the Navier-Stokes equations in three dimensions. In this talk, we exhibit two distinct Leray solutions with zero initial velocity and identical body force. Building on a recent work of Vishik, we construct a linear unstable self-similar solution to the 3D Navier-Stokes with force. We employ the linear instability of the latter to build the second solution, which is a trajectory on the unstable manifold, in accordance with the predictions of Jia and Šverák. -- Indico :: Email Notifier https://events.dm.unipi.it/e/100

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Analysis-seminar October 2022