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Analysis of Geometrical Effects on Dispersive Equations

Total Cost €


EC-Contrib. €






 ANADEL project word cloud

Explore the words cloud of the ANADEL project. It provides you a very rough idea of what is the project "ANADEL" about.

concentration    quantum    context    manifolds    extend    pdes    sometimes    dispersion    ones    rough    theoretic    last    tomography    nonlinear    first    arbitrarily    boundary    packets    quantitative    birth    approximate    technologies    decade    dispersive    clusters    significantly    spreading    localization    ouml    harmonic    linear    singularities    computed    name    fiber    infinity    eigenfunctions    motivations    progress    tools    solutions    dinger    quasilinear    background    equations    wave    dealing    space    mathematical    compact    appear    sonar    optic    sharp    chaos    parametrices    direct    caustics    despite    exist    good    hyperbolic    bounds    heart    naturally    theory    geometric    questions    concerned    independent    life    microlocal    limited    propagation    heterogeneous    waves    motivated    homogeneous    pointwise    functions    physically    settings    boundaries    toy    physics    refinements    models    radar    efficient    earlier    green    schr    respect    curved    connections    influence    scope    media    few   

Project "ANADEL" data sheet

The following table provides information about the project.


Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙293˙763 €
 EC max contribution 1˙293˙763 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-STG
 Funding Scheme ERC-STG
 Starting year 2018
 Duration (year-month-day) from 2018-02-01   to  2023-01-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

We are concerned with localization properties of solutions to hyperbolic PDEs, especially problems with a geometric component: how do boundaries and heterogeneous media influence spreading and concentration of solutions. While our first focus is on wave and Schrödinger equations on manifolds with boundary, strong connections exist with phase space localization for (clusters of) eigenfunctions, which are of independent interest. Motivations come from nonlinear dispersive models (in physically relevant settings), properties of eigenfunctions in quantum chaos (related to both physics of optic fiber design as well as number theoretic questions), or harmonic analysis on manifolds.

Waves propagation in real life physics occur in media which are neither homogeneous or spatially infinity. The birth of radar/sonar technologies (and the raise of computed tomography) greatly motivated numerous developments in microlocal analysis and the linear theory. Only recently toy nonlinear models have been studied on a curved background, sometimes compact or rough. Understanding how to extend such tools, dealing with wave dispersion or focusing, will allow us to significantly progress in our mathematical understanding of physically relevant models. There, boundaries appear naturally and most earlier developments related to propagation of singularities in this context have limited scope with respect to crucial dispersive effects. Despite great progress over the last decade, driven by the study of quasilinear equations, our knowledge is still very limited. Going beyond this recent activity requires new tools whose development is at the heart of this proposal, including good approximate solutions (parametrices) going over arbitrarily large numbers of caustics, sharp pointwise bounds on Green functions, development of efficient wave packets methods, quantitative refinements of propagation of singularities (with direct applications in control theory), only to name a few important ones.

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