14:00h – 14:40h

Non-Invasive Imaging Using Numerical Techniques Based on Topological Derivates

The challenge of identifying the location, size, and shape of objects embedded within a medium has garnered significant attention in recent years. This issue is critically important across various fields, including medical imaging, non- destructive material testing, and natural resource exploration. In this presentation, we will introduce numerical methods based on topological derivative computations for detecting multiple defects. These methods generate indicator functions that can classify each point in the region of interest as either part of the background medium or an object, without any prior assumptions
about the number, size, shape, or location of the objects. The effectiveness of the method will be illustrated across various applications, including acoustic, electromagnetic, and thermographic inspections.

14:50h – 15:30h

The binormal flow and the evolution of viscous vortex filaments 

14:00h – 14:40h

Tracking controllability for finite-dimensional linear systems.

14:50h – 15:30h

Generalized Convolution Quadrature for non smooth sectorial problems

 We consider the application of the generalized Convolution Quadrature (gCQ) to approximate the solution of an important class of sectorial problems. The gCQ is a generalization of  Lubich’s Convolution Quadrature (CQ) that allows for variable steps. The available stability and convergence theory for the gCQ requires non realistic regularity assumptions on the data, which do not hold in many applications of interest, such as the approximation of subdiffusion equations. It is well known that for non smooth enough data the original CQ, with uniform steps, presents an order reduction close to the singularity. We generalize the analysis of the gCQ to data satisfying realistic regularity assumptions and provide sufficient conditions for stability and convergence on arbitrary sequences of time points. We consider the particular case of graded meshes and show how to choose them optimally, according to the behaviour of the data. An important advantage of the gCQ method is that it allows for a fast and memory reduced implementation. We describe how the fast and oblivious gCQ can be implemented and illustrate our theoretical results with several numerical experiments.

14:00h – 14:40h

Semiclassical Homogenization in the Problem of Localized Linear Waves Propagation

14:50h – 15:30h

Asymptotic behavior of solutions for some diffusion problems on metric graphs

14:00h – 14:40h

On the reachable space for the heat equation.

The goal of this talk is to explain how perturbative arguments can be applied to derive a sharp description of the reachable space for heat equations having lower order terms. The main result I will present is the following one. Let us consider an abstract system $y’ = Ay + Bu$, where $A$ is an operator generating a $C^0$ semigroup $(exp(tA))_{t\geq 0}$ on a Hilbert space $X$, and $B$ is a control operator, for instance a linear operator from an Hilbert space $U$ to $X$, and let us assume that this system is null-controllable in $X$ in any positive time. Then, setting $R$ the reachable set of the system (that is all the states that can be achieved by $y$ solution of $y’ = Ay + Bu$, $y(0) = 0$), the restriction of $(exp(tA))_{t \geq 0}$ to $R$ forms a $C^0$ semigroup on $R$. Accordingly, the system $y’ = Ay + Bu$ is exactly controllable on $R$, and one can then perform classical perturbative arguments to handle lower order terms, as I will explain on a few examples. This talk is based on a joint work with Kévin Le Balc’h (INRIA Paris) and Marius Tucsnak (Bordeaux).

14:50h – 15:30h

Two-Scale Pic Methods as an Alternative to Gyro-Kinetic Simulations

 Numerical methods for simulations of particles’ trajectories under magnetic confinement based on two-scale expansion of those trajectories are very comprehensive. Yet, their implementations are heavy since the resulting system for the two scale expanded trajectories has a heavy right hand side. This is certainly the reason why the computations made 20 years ago for those implementations were left unapplied. 

14:00h – 14:40h

Stability of abstract thermoelastic delayed systems

In this talk, a stabilization problem for a generalized thermoelastic system with delay, known as the $\alpha-\beta$ system, is addressed. The well-posedness of the system is proven using the semigroup approach. Under certain conditions, exponential and polynomial stability of the system is established via a frequency-domain approach. These theoretical results are then applied to specific examples in thermoelasticity.

14:50h – 15:30h

Asymtotic behavior of positive solutions for a degenerate logistic equation with mixed local and non-local diffusion

14:00h – 14:40h

Random Batch Methods for Optimal Control of Networked 1D Hyperbolic Systems

 Optimal control for networks of hyperbolic systems is important in many
applications, such as gas networks, flexible multi-body systems, and
water networks. However, solving such optimal control problems can be
computationally demanding when the network is large or contains loops.
In this talk, we present new convergence results for the simulation and
optimal control of 1D hyperbolic systems by the Random Batch Method
(RBM). The RBM is a recently proposed randomized operator-splitting
technique inspired by the successes of stochastic algorithms in machine
learning [Shi Jin, Lei Li, Jian-Guo Liu, J. of Comp. Phys. , 2020]. The
results in this talk are the first extension of the analysis for
finite-dimensional optimal control problems in [Veldman, Zuazua, Numer.Math., 2022] to hyperbolic partial differential equations. A numerical example for a network with loops shows that the proposed method reduces the computational cost significantly.

14:50h – 15:30h

Local and global null controllability of a nonlinear
parabolic system with a multiplicative control in moving
domains