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10 papers · 2 filters
Blowing-up solutions for second-order critical elliptic equations: the impact of the scalar curvature
Frédéric Robert, Jérôme Vétois
Given a closed manifold , , Olivier Druet proved that a necessary condition for the existence of energy-bounded blowing-up solutions to perturbations of the equat…
Boundary value problems for elliptic partial differential equations
Mourad Choulli
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elli…
Existence of contacts for the motion of a rigid body into a viscous incompressible fluid with the Tresca boundary conditions
Matthieu Hillairet, Takéo Takahashi
We consider a fluid-structure interaction system composed by a rigid ball immersed into a viscous incompressible fluid. The motion of the structure satisfies the Newton laws and th…
Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions
Claudia Gariboldi, Takéo Takahashi
We consider an optimal control problem for the Navier-Stokes system with Navier slip boundary conditions. We denote by the friction coefficient and we analyze the asymptotic be…
Stabilization of a rigid body moving in a compressible viscous fluid
Arnab Roy, Takéo Takahashi
We consider the stabilizability of a fluid-structure interaction system where the fluid is viscous and compressible and the structure is a rigid ball. The feedback control of the s…
Inverse problems for Schrödinger equations with unbounded potentials
Mourad Choulli
We summarize in these notes the course given at the Summer School of AIP 2019 held in Grenoble from July 1st to July 5th. This course was mainly devoted to the determination of the…