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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.

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

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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lastchecktime (2020-10-01 1:10:02) correctly updated