Seminars and Colloquia by Series

TBA by Abdon Moutinho

Series
PDE Seminar
Time
Tuesday, February 28, 2023 - 15:00 for 1 hour (actually 50 minutes)
Location
Online: https://gatech.zoom.us/j/95574359880?pwd=cGpCa3J1MFRkY0RUeU1xVFJRV0x3dz09
Speaker
Abdon MoutinhoLAGA, Université Sorbonne Paris Nord

TBA

Regularity of Hele-Shaw flow with source and drift: Flat free boundaries are Lipschitz

Series
PDE Seminar
Time
Tuesday, February 14, 2023 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yuming Paul ZhangAuburn University

The classical Hele-Shaw flow describes the motion of incompressible viscous fluid, which occupies part of the space between two parallel, nearby plates. With source and drift, the equation is used in models of tumor growth where cells evolve with contact inhibition, and congested population dynamics. We consider the flow with Hölder continuous source and Lipschitz continuous drift. We show that if the free boundary of the solution is locally close to a Lipschitz graph, then it is indeed Lipschitz, given that the Lipschitz constant is small. This is joint work with Inwon Kim.

Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons

Series
PDE Seminar
Time
Tuesday, February 7, 2023 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jessica Trespalacios JulioUniversidad de Chile

We consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth global solutions inside the light cone. Finally, some applications are presented in the case of PCF solitons, a first step towards the study of its nonlinear stability. 

Optimal control of stochastic delay differential equations

Series
PDE Seminar
Time
Tuesday, January 31, 2023 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Filippo de FeoPolitecnico di Milano

In this talk we will discuss an optimal control problem for stochastic differential delay equations. We will only consider the case with delays in the state. We will show how to rewrite the problem in a suitable infinite-dimensional Hilbert space. Then using the dynamic programming approach we will characterize the value function of the problem as the unique viscosity solution of an infinite dimensional Hamilton-Jacobi-Bellman equation.  We will discuss partial C^{1}-regularity of the value function. This regularity result is particularly interesting since it permits to construct a candidate optimal feedback map which may allow to find an optimal feedback control. Finally we will discuss some ideas about the case in which delays also appear in the controls.

This is a joint work with S. Federico and A. Święch.

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