I am interested in partial differential equations and in the qualitative study of the infinite dimensional systems, which they generate. Such a study required to work in various domains. In a general way, I am also interested in the qualitative behaviour of models issued from physic or biology and in all what confirms in a mathematical way an intuition or observation on real phenomena.

## Reseach articles

Generic dynamics of dissipative PDE:- Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations, with Pavol Brunovský and Geneviève Raugel, published in the Journal of Dynamics and Differential Equation n.34 (2022), p. 2639-2679.
- A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations, with Geneviève Raugel, published in Confluentes Mathematici n.3 (2011), p. 471-493.
- Generic Morse-Smale property for the parabolic equation on the circle, with Geneviève Raugel, published in the Annales de l'IHP, Analyse Non Linéaire n.27 (2010), p. 1397-1440.
- Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle, with Geneviève Raugel, published in the Transactions of the AMS n.362 (2010), p. 5189-5211.
- Adaptation of the generic PDE's results to the notion of prevalence, published in the Journal of Dynamics and Differential Equations n.19 (2007), p. 967-983.
- Generic transversality property for a class of wave equations with variable damping, published in Journal de Mathématiques Pures et Appliquées n.84 (2005), p. 1015-1066.

- Decay of semilinear damped wave equations: cases without geometric control condition, with Camille Laurent published in the Annales Henri Lebesgue n.3 (2020), p. 1241-1289..
- Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation, with Julien Royer, published in Journal of the Mathematical Society of Japan n.70 (2018), p. 1375-1418.
- Exponential decay for the damped wave equation in unbounded domains, with Nicolas Burq, published in Communications in Contemporary Mathematics n.18 (2016), p. 1650012.
- A note on the global controllability of the semilinear wave equation, with Camille Laurent, published in SIAM Journal on Control and Optimization n.52 (2014), p. 439-450.
- Stabilization for the semilinear wave equation with geometric control condition, with Camille Laurent, published in Analysis and PDE n.6 (2013), p. 1089-1119.
- New examples of damped wave equations with gradient-like structure, published in Asymptotic Analysis n.53 (2007), p. 237-253.
- Convergence of the wave equation damped on the interior to the one damped on the boundary, published in Journal of Differential Equations n.229 (2006), p. 588-653.

- Control of the SchrÃ¶dinger equation by slow deformations of the domain, with Alessandro Duca and Dmitry Turaev, Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire (2023).
- Schrödinger equation in moving domains, with Alessandro Duca, published in the Annales Henri Poincaré n.22 (2021), p. 2029-2063.
- Permuting quantum eigenmodes by a quasi-adiabatic motion of a potential wall, with Alessandro Duca and Dmitry Turaev, published in Journal of Mathematical Physics n.61 (2020), 101511.

- Generic transversality of travelling fronts, standing fronts and standing pulses for parabolic gradient systems, with Emmanuel Risler, manuscript.
- Asymptotic self-similarity in diffusion equations with nonconstant radial limits at infinity, with Thierry Gallay and Geneviève Raugel, published in the Journal of Dynamics and Differential Equation n.34 (2022), p. 2593-2638.
- Asymptotic profiles for a travelling front solution of a biological equation, with Guillemette Chapuisat, published in Mathematical Models and Methods in Applied Sciences, n.21 (2011) p. 2155-2177.
- Global stability of travelling fronts for a damped wave equation with bistable nonlinearity, with Thierry Gallay, published in the Annales Scientifiques de l'Ecole Normale Supérieure n.42 (2009), p. 103-140.

- Observation and inverse problems in coupled cell networks, published in Nonlinearity n.25 (2012), p. 657-676.
- How opening a hole affects the sound of a flute, published in Journal of Spectral Theory n.1 (2011), p. 389-408.

## Other articles

- In memoriam: GeneviÃ¨ve Raugel, with Adriana Valentina Busuioc and Thierry Gallay, published in the Journal of Dynamics and Differential Equation n.34 (2022), p. 2585-2592.

## Academic works

- Habilitation thesis (french), intitled
*Dynamique des EDP dissipatives*.