Mazanti, Guilherme Boussaada, Islam Niculescu, Silviu-Iulian Chitour, Yacine

It has been observed in several recent works that, for some classes of linear time-delay systems, spectral values of maximal multiplicity are dominant, a property known as multiplicity-induced-dominancy (MID). This paper starts the investigation of whether MID holds for delay differential-algebraic systems by considering a single-delay system compo...

Canon, Éric Chardard, Frédéric Panasenko, Grigory Štikonienė, Olga

A non-stationary flow in a network of thin tubes is considered. Its one-dimensional approximation was proposed in a paper by G.Panasenko and K.Pileckas, Flows in a tube structure: equation on the graph, JMP (2014). It consists of a set of equations with weakly singular kernels, on a graph, for the macroscopic pressure. A new difference scheme for t...

Calatroni, Luca Lanza, Alessandro Pragliola, Monica Sgallari, Fiorella

We propose an efficient estimation technique for the automatic selection of locally-adaptive Total Variation regularisation parameters based on an hybrid strategy which combines a local maximum-likelihood approach estimating space-variant image scales with a global discrepancy principle related to noise statistics. We verify the effectiveness of th...

Mrad, Mohamed

The method of characteristics is a powerful tool to solve some nonlinear second order stochastic PDEs like those satisfied by a consistent dynamic utilities, see [EM13, MM20]. In this situation the solution V (t, z) is theoretically of the formX t V (0,ξ t (z)) whereX and Y are solutions of a system of two SDEs,ξ is the inverse flow ofȲ and V (0, ....

Mouzard, Antoine Zachhuber, Immanuel

We prove Strichatz inequalities for the Schrödinger equation and the wave equation with multiplicative noise on a two-dimensional manifold. This relies on the Anderson Hamiltonian H described using high order paracontrolled calculus. As an application, it gives a low regularity solution theory for the associated nonlinear equations.

Delort, Jean-Marc Masmoudi, Nader

Bristeau, Marie-Odile Di Martino, Bernard Mangeney, Anne Sainte-Marie, Jacques Souillé, Fabien

In this paper, we propose several time dependent analytical solutions for the incompressible Euler and Navier-Stokes systems with free surface. The given analytical solutions concerns the hydrostatic and non-hydrostatic Euler and Navier-Stokes systems.

Boyaval, Sébastien Dostalík, Mark

We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using additional structure variables. It is obtained by writing the Helmholtz free energy as the sum of a volumetric ene...

Beauchard, Karine Le Borgne, Jérémy Marbach, Frédéric

Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to decouple time-dependent features from geometry-dependent features of the solution have been extensively studied. ...

Baty, Hubert Drui, Florence Franck, Emmanuel Helluy, Philippe Klingenberg, Christian Tannhaüser, Lukas

This paper is devoted to the simulation of MHD flows with complex structures. This kind flows present instabilities that generate shock waves. We propose a robust and precise numerical method based on the Lattice Boltzmann methodology. We explain how to adjust the numerical viscosity in order to obtain stable, precise results and reduced divergence...