KIT - Department of Mathematics - Dr. Louis Garénaux

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Department of Mathematics

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Institute for Analysis

Workgroup Nonlinear Partial Differential Equations

Dr. Louis Garénaux

Part 2 of the Ringvorlesung is based on these notes. The detailed discussion for each session is as follows.

My research focuses on evolution PDE, and can be briefly summarized with the following keywords:

dispersive-diffusive equations, balance laws, reaction-diffusion equations, discrete space domains
existence of solutions, 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. Hilder — Linear convective stability of a front superposition with unstable connecting state. arXiv
L. Garénaux and H. J. Hupkes — Existence of monostable fronts for a KPP infinite-difference numerical scheme. arXiv
L. Garénaux and B. de Rijk — Long time behavior of small solutions in the viscoelastic 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). DOI - 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

Updated March 2025.