Guillaume Warnault

Guillaume Warnault is a Lecturer at the University of Pau and Pays de l'Adour since September 2010, affiliated with the Analysis, Geometry and Applications research team within the Laboratory of Mathematics and their Applications (LMAP). Previously, he held a Temporary Teaching and Research Associate position at François Rabelais University, Tours (2009-2010) following doctoral studies at the University of Picardie Jules Verne.

Education:

• Doctorate in Mathematics, University of Picardie Jules Verne, Amiens (2006-2009). Thesis: "Stable solutions for semilinear elliptical PDEs involving the biharmonic operator".

Research Focus: His work centers on nonlinear partial differential equations, particularly elliptic and parabolic systems, biharmonic operators, and problems with variable exponents. Key contributions include blow-up analysis for quasilinear systems, regularity theory for fractional Laplacian equations, and bifurcation phenomena in singular biharmonic problems. His research bridges pure analysis with applications in fluid dynamics and mathematical physics.

Publication Trends: Recent work (2016-2022) shows deepening specialization in p(x)-homogeneous operators and fractional calculus, with increasing collaboration intensity. Over 80% of his publications involve co-authors Giacomoni and Arora, reflecting sustained research partnerships. His output demonstrates methodological consistency in applying variational techniques to nonlinear PDEs while expanding into emerging areas like doubly nonlinear systems.

Academic Leadership: Warnault serves as program director for the Master's in Mathematics, Modeling and Simulation (MMS) since 2023 and previously directed the MAISHS undergraduate program (2019-2023). He has supervised six Master's theses and co-directed Rakesh Arora's PhD (2017-2020). As an elected laboratory council member since 2012 and former committee of experts member (2012-2020), he actively shapes institutional research strategy.

Research Environment: Based at the IPRA Building in Pau, he contributes to LMAP (UMR 5142), a CNRS-affiliated laboratory fostering interdisciplinary work in mathematical analysis and its applications through the Analysis, Geometry and Applications team.