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Dr. Louis Garénaux

  • 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.

My research focuses on evolution PDE, and can be briefly summarize 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.

Preprints

  • L. Garénaux and B. de Rijk — Long time behavior of small solutions in the viscous Klein-Gordon equation. arXiv
  • L. Garénaux and L. M. Rodrigues — Convective stability in scalar balance laws. 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 — 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

Conferences

  • 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

  • 2023: PDE seminar, Nancy, France
  • 2022: Math-bio, Orléans, France
  • 2021: PDE seminar Rennes, France
  • 2020: Stuttgart, Germany

Updated May 2024.