François Samer Genoud

Biographie

2000-2005 Etudes en Physique à l'EPFL dont une année d'échange à Zürich (ETH, 2002-2003). 2005 Diplôme de Physicien EPF (Master) en physique mathématique, sous la direction du Prof. C.-E. Pfister. 2005-2008 Doctorat sous la direction du Prof. C.A. Stuart, sur l'étude de certaines équations de Schrödinger non-linéaires, en particulier de questions liées à l'existence et la stabilité orbitale d'ondes stationnaires. 2009-2010 Chercheur postdoc FNS à OxPDE, Université d'Oxford. 2010-2013 Chercheur postdoc à l'Université Heriot-Watt, Edimbourg. 2013-2014 Chercheur postdoc à l'Université de Vienne. 2015-2017 Professeur Assistant à TU Delft. 2017-2018 Professeur Associé à l'Université libre de Bruxelles. 2018- Directeur du CMS Domaines d'intérêt scientifique: analyse non-linéaire, calcul des variations, équations aux dérivées partielles, physique mathématique et physique théorique en général.

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https://people.epfl.ch/francois.genoud?lang=fr

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Stability of standing waves for a nonlinear Klein-Gordon equation with delta potentials

François Samer Genoud

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike the unperturbed case, a noteworthy difficulty here arises from the possible non-unitarity of the semigroup generating the corresponding linear evolution. We then show that the equation is Hamiltonian and we establish several stability/instability results for its standing waves. Our analysis relies on a detailed study of the spectral properties of the linearization of the equation, and on the well-known 'slope condition' for orbital stability. (C) 2019 Elsevier Inc. All rights reserved.

2019

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The following nonlinear Schrodinger equation is studied

2009

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Existence And Stability Of High Frequency Standing Waves For A Nonlinear Schrodinger Equation

François Samer Genoud

This article is concerned with the existence and orbital stability of standing waves for a nonlinear Schrodinger equation (NLS) with a nonautonomous nonlinearity. It continues and concludes the series of papers [6, 7, 8]. In [6], the authors make use of a continuation argument to establish the existence in R x H-1(R-N) of a smooth local branch of solutions to the stationary elliptic problem associated with (NLS) and hence the existence of standing wave solutions of (NLS) with small frequencies. Complementary conditions on the nonlinearity are found, under which either stability of the standing waves and bifurcation of the branch of solutions from the point (0, 0) is an element of R x H-1 (R-N) occur, or instability and asymptotic bifurcation occur. The main hypotheses in [6] concern the behaviour of the nonlinearity with respect to the space variable at infinity. The paper [7] extends the results of [6] to (NLS) with more general nonlinearities. In [8], the global continuation of the local branch obtained in [6] is proved under additional hypotheses on the nonlinearity. In particular, spherical symmetry with respect to the space variable is assumed. The aim of the present work is to prove the existence and discuss the orbital stability of standing waves with high frequencies, independently of the results obtained in [6] and [8]. The main hypotheses now concern the behaviour of the nonlinearity with respect to the space variable around the origin. The methods are the same in spirit as that of [6] and permit to discuss the asymptotic behaviour of the global branch of solutions obtained in [8].

2009

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