Dr. Louis Garénaux
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Kollegiengebäude Mathematik (20.30)
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+49 721 608 43193
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louis.garenaux@kit.edu
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Englerstrasse 2
76131 Karlsruhe
Germany
I currently work as a post-doc at Karlsruhe Institut für Technologie, in the wave phenomena Collaborative Research Center. I am part of the projects A14, AP8, and of the junior research group stability of nonlinear waves.
Between July 15th and November 1st 2024, I work from Leiden Mathematical Institute, in office B.W.1.37.
My research focuses on evolution PDE, and can be briefly summarized with the following keywords:
- dispersive-diffusive equations, balance laws, reaction-diffusion equations,
- global well-posedness, asymptotic stability, spectral stability,
- normal form transform, space-time resonances, amplitude equations, Duhamel formulation, resolvent kernel bounds.
Research texts
Preprints
- L. Garénaux and B. de Rijk — Long time behavior of small solutions in the viscous Klein-Gordon equation. arXiv
- L. Garénaux and B. de Rijk — Global existence and decay of small solutions in a viscous half Klein–Gordon equation, CRC 1173 Preprint 2022/80, Karlsruhe Institute of Technology (2022). pdf
Publications
- L. Garénaux and L. M. Rodrigues — Convective stability in scalar balance laws, Differential Integral Equations 38, 1-2 (2025). arXiv
- L. Garénaux — Nonlinear convective stability of a critical pulled front undergoing a Turing bifurcation at its back: a case study, SIAM J. Math. Anal. 56, 3 (2024). DOI - arXiv
- M. Avery and L. Garénaux — Spectral stability of the critical front in the extended Fisher-KPP equation, Z. Angew. Math. Phys. 74, 71 (2023). DOI - arXiv
Memoir
- PhD thesis — Asymptotic stability of invasion fronts in reaction-diffusion equations (2022). HAL
Presentations
Conferences
- 2024: workshop — Dynamical system approach towards nonlinear PDEs, Stuttgart, Germany
- 2024: Equadiff conference, Karlstad, Sweden
- 2023: SIAM conference — Application of Dynamical Systems, Portland, Oregon
- 2022: workshop — Women in PDEs, Karlsruhe, Germany
- 2022: workshop — Spatial dynamics and related approaches, Stuttgart, Germany
- 2022: SIAM conference — Nonlinear Waves and Coherent Structures, Bremen, Germany
- 2021: workshop — MAMOVI days, Saclay, France
- 2021: winter school — Non-local models arising from biology, CIRM, Marseille, France
- 2021: conference — Dynamics Days Europe, Nice, France
- 2020: winter school — PDE and probability for biology, CIRM, Marseille, France
Local seminars
- 2024: Dynamical System seminar, Leiden, The Netherlands
- 2024: MOCO seminar, Strasbourg, France
- 2023: PDE seminar, Nancy, France
- 2022: Math-bio seminar, Orléans, France
- 2021: PDE seminar, Rennes, France
- 2020: Oberseminar, Stuttgart, Germany
On site
- Karlsruhe, Germany: x5
- Toulouse, France: x6
Updated September 2024.