Seminars take place in the seminar room, first floor of the building Le Chablais, (see How to come ?).

Next seminar:

Friday 31st March 2023 at 14h Marie Amélie Morlais (Université du Maine),
Optimal switching problems and related systems of PDEs with (interconnected) obstacles.

Abstract: (Hide abstracts)
This talk shall focus on the presentation of a (by now) well studied research topic in the field of stochastic control theory, i.e the case of optimal switching control problems. A main objective of this talk is to provide the connection with system of semilinear PDEs with obstacles which, in addition, are inter- connected. This last feature (among some others) explains why the solution is not smooth (in general). For this reason we study existence and uniqueness of solutions of these PDEs in viscosity sense. In a first part, we shall explain the relationship between the value functional associated with a stochastic control problem and the solution of an explicit semi- linear PDE. For this, we need to introduce both the stochastic framework and some advanced probabilistic tools & technics. Next and after this introductory part, we shall give the precise structure of the system of PDEs we are interested in and provide some theoretical results. If time allows, the last slides present the main steps of one of our main results. This talk is based on several joint works (with Pr. S. Hamadène (LMM), Pr. B Djehiche (KTH Stockholm) and X. Zhao former pHD student at the LMM).

The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.
Settings: See with decreasing date. Hide abstracts
Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, all years together.

Year 2023

Friday 10th February 2023 at 14h Christoph Walker (Institut für angewandte Mathematik, Leibniz, Univ Hannover),
Age-Dependent Populations with Spatial Diffusion

Abstract: (Hide abstracts)
A prototypical model for an age-structured diffusive population is considered in which individuals are distinguished by age and spatial position. The evolution equation involves a diffusion term for the space variable and a transport term for the age variable supplemented with a nonlocal boundary condition. The linear version of the model gives rise to a strongly continuous semigroup which exhibits the parabolic regularizing effects in the space variable. We determine its asymptotic behavior based on spectral properties of the associated generator. For a nonlinear version of the model we investigate the existence of nontrivial steady states and establish a principle of linearized stability.

Friday 3rd March 2023 at 09h30 B. Bogosel (Ecole Polytechnique),
GdT FOPDI : Accessibility constraints in shape optimization

Friday 3rd March 2023 at 10h M. Nahon (Max Planck, Leipzig),
GdT FOPDI : Stability of higher order Dirichlet eigenvalues

Friday 3rd March 2023 at 10h30 R. Prunier (IMJ, Sorbonne),
GdT FOPDI : Stability in shape optimization

Friday 3rd March 2023 at 11h V. Amato (Univ Naples, Italy),
GdT FOPDI : Sharp quantitative Poincaré inequality

Friday 24th March 2023 at 10h45 Francois Nicot (Univ Savoie Mont-Blanc),
Failure in geomaterials: an emerging process through successive scales

Abstract: (Hide abstracts)
Solving boundary value problems requires implementation of sufficiently robust constitutive models. Most models try to incorporate a great deal of phenomenological ingredients, but this refining often leads to overcomplicated mathematical formulations, requiring a large number of parameters to be identified. On the other hand, geomaterials are known to have an internal microstructure, made up of an assembly of interacting particles. Most of the macroscopic properties, observed on a specimen scale or even on larger scales, mainly result from the microstructural arrangement of grains. Thus, a powerful alternative can be found with micromechanical models, where the medium is described as a distribution of elementary sets of grains. The inherent complexity is not related to the local constitutive description between particles in contact, but to the basic topological complexity taking place within the assembly. This presentation discusses this issue, highlighting very recent results obtained from discrete element simulations. In particular, the so-called critical state regime that develops during localized or diffuse failure is discussed in detail from the perspective of emerging processes taking place within complex media.

Friday 31st March 2023 at 14h Marie Amélie Morlais (Université du Maine),
Optimal switching problems and related systems of PDEs with (interconnected) obstacles.

Abstract: (Hide abstracts)
This talk shall focus on the presentation of a (by now) well studied research topic in the field of stochastic control theory, i.e the case of optimal switching control problems. A main objective of this talk is to provide the connection with system of semilinear PDEs with obstacles which, in addition, are inter- connected. This last feature (among some others) explains why the solution is not smooth (in general). For this reason we study existence and uniqueness of solutions of these PDEs in viscosity sense. In a first part, we shall explain the relationship between the value functional associated with a stochastic control problem and the solution of an explicit semi- linear PDE. For this, we need to introduce both the stochastic framework and some advanced probabilistic tools & technics. Next and after this introductory part, we shall give the precise structure of the system of PDEs we are interested in and provide some theoretical results. If time allows, the last slides present the main steps of one of our main results. This talk is based on several joint works (with Pr. S. Hamadène (LMM), Pr. B Djehiche (KTH Stockholm) and X. Zhao former pHD student at the LMM).

Friday 5th May 2023 at 14h Francesco Fanelli (Univ Claude Bernard Lyon 1),
à venir

Friday 26th May 2023 at 14h Christel Geiss (University of Jyväskylä),
à venir

Friday 30th June 2023 at 14h Khawla Msheik (Univ Claude Bernard Lyon 1),
New mathematical model for Tsunamis with precise time arrival predictions

Abstract: (Hide abstracts)
We propose a new system of equations modeling Tsunamis in this work. It is a coupled system accounting for both water compressibility and viscoelasticity of the earth. Adding these latter physical effects is responsible for the closest-to-reality time arrival predictions (among existing models), capturing the negative peak before the main wave hump, and exhibiting the negative dispersion phenomena. This comes in remarkable agreement with previous experiments and studies on the topic. The system is also delivered in a relatively simple mathematical structure of equations that is easy to solve numerically.

The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.
Settings: See with decreasing date. Hide abstracts
Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, all years together.