Analysis and Modelling

This team studies PDE from the theoretical and numerical viewpoints, for applications to Physics and Life Sciences.

Permanent members
Emmanuel Grenier, Nicolas Rougerie (Head of the team), Laure Saint-Raymond, Denis Serre, Sergio Simonella, Paul Vigneaux, Julien Vovelle

Post-Docs, AGPR, PhD students
Paul Alphonse, Clément Berger, Van Duong Dinh, Corentin Le Bihan, Dinh-Thi Nguyen, Denis Perice, Jules Pitcho, Valentine Roos (30%), Raphael Winter, Qiyun Yang, Simon Zugmeyer

Research themes
- existence of solutions and their qualitative properties - stability, asymptotic behaviour
- quantitative analysis (travelling waves, ...)
- development and study of numerical schemes
- parameters estimation via bayesian methods for PDEs

Applications domains
- physics and fluid mechanics, geophysics
- biology and medecine, ecology

Project-team INRIA - NUMED (Numerical Medicine)
Headed by Emmanuel Grenier from 2008 to 2021, this project-team has for aim to develop complex mathematical models (based on partial differential equations) to simulate the evolution of several pathologies (cancer, stroke) integrating heterogeneous data coming from different scales (molecular pathway, cell, tissue, organ, ...) and taking into account the spatiality of the biological phenomena. Numerical simulation techniques coupled to parameter estimation methods aim at predicting and optimizing therapies efficacy. Website

Projets & Contrats
- ERC starting grant MESOPROBIO (2015-2020), PI : Vincent Calvez + Jimmy Garnier (U. de Savoie) + Sepideh Mirrahimi (U. de Toulouse)
- FP7 Project DDMore (2011-2016)
- ANR : VPFlows (2021-2025), PI : Paul Vigneaux ; ADA (2019-2024), PI : Julien Vovelle ; MODPOL (2012-2015), PI : Vincent Calvez ; RUGO (2009-2012) ; SECHELLES (2009-2012) ; BIMBO (2009-2011) ; AVC in Silico (2006-2010), PI : Emmanuel Grenier
- CNRS: TELLUS Insu-Insmi (2016) ; Défi Interdisciplinaire InFIniti (2017 and 2018) on Viscoplastic Fluids, PI : Paul Vigneaux
- Plan Cancer - Math-Info (MIC) : PI : Emmanuel Grenier (2019)
- Industrial contracts : L'Oréal, Sanofi Pasteur, Merial, Servier

Scientific activities
- Joint Seminar with ICJ :"PDE, Modelling and Scientific Computing", 2 seminars every two weeks, on Tuesday at 14h and 15h15 (alternatively at ENSL and at Lyon 1)
- JERAA : PDE days Rhône-Alpes-Auvergne (each year, Oct-Nov). Website
- GdR CNRS MathGeoPhy (2022-2026)

Popularization
- Itinerant exhibitions in high schools : MathaLyon
- Editorial activity for the CNRS' mathematical popularization website : "Images des Maths" : http://images.math.cnrs.fr/
- European Heritage days 2017 (Sept 16-17) at ENS de Lyon: popularization talks with the public (here). "80 ans" of CNRS in 2019.