Publications and preprints

[33] P. Gabriel, B. van Brunt, G. C. Wake and A. A. Zaidi. Spectral description of a cell growth and division equation. arXiv:2409.14903 (2024).

[32] B. Cloez, A. El Abdouni and P. Gabriel. The principal eigenvalue problem for time-periodic nonlocal equations with drift. arXiv:2409.01868 (2024).

[31] K. Carrapatoso, P. Gabriel, R. Medina and S. Mischler. Constructive Krein-Rutman result for kinetic Fokker-Planck equations in a domain. arXiv:2407.10530 (2024).

[30] C. Fonte Sanchez, P. Gabriel, and S. Mischler. On the Krein-Rutman theorem and beyond. arXiv:2305.06652 (2023).

[29] B. Cloez and P. Gabriel. Fast, slow convergence, and concentration in the house of cards replicator-mutator model. Differential Integral Equations, Vol.37, No.7-8 (2024), pp.547-584.

[28] M. Alfaro, P. Gabriel, and O. Kavian. Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics. Discrete Contin. Dyn. Syst. Ser. B, Special issue in memory of Masayasu Mimura, Vol.28, No.12 (2023), pp.5905-5933.

[27] J. A. Cañizo, P. Gabriel, and H. Yoldaş. Spectral gap for the growth-fragmentation equation via Harris's theorem. SIAM J. Math. Anal., Vol.53, No.5 (2021), pp.5185-5214.

[26] P. Gabriel and H. Martin. Periodic asymptotic dynamics of the measure solutions to an equal mitosis equation. Ann. H. Lebesgue, Vol. 5 (2022), pp.275-301.

[25] B. Cloez and P. Gabriel. On an irreducibility type condition for the ergodicity of nonconservative semigroups. C. R. Math. Acad. Sci. Paris, Vol. 358, No.6 (2020), pp.733-742.

[24] V. Bansaye, B. Cloez, P. Gabriel, and A. Marguet. A non-conservative Harris ergodic theorem. J. Lond. Math. Soc., Vol. 106, No. 3 (2022), pp.2459-2510.

[23] É. Bernard and P. Gabriel. Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate. J. Evol. Equ., Vol.20, No.2 (2020), pp.375-401.

[22] P. Gabriel and H. Martin. Steady distribution of the incremental model for bacteria proliferation. Netw. Heterog. Media, Special issue on mathematical methods in systems biology, Vol.14, No.1 (2019), pp.149-171.

[21] V. Bansaye, B. Cloez, and P. Gabriel. Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions. Acta Appl. Math., Vol.166 (2020), pp.29-72.

[20] G. Dumont and P. Gabriel. The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states. Nonlinearity, Vol.33 (2020), pp.6381-6420.

[19] P. Gabriel. Measure solutions to the conservative renewal equation. ESAIM Proc. Surveys, CIMPA School on Mathematical Models in Biology and Medicine, Vol.62 (2018), pp.68-78.

[18] V. Calvez, P. Gabriel, and Á. Mateos González. Limiting Hamilton-Jacobi equation for the large scale asymptotics of a subdiffusion jump-renewal equation. Asymptot. Anal., Vol.115, No.1-2 (2019), pp.63-94.

[17] É. Bernard, M. Doumic, and P. Gabriel. Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts. Kinetic Related Models, Vol.12, No.3 (2019), pp.551-571.

[16] É. Bernard and P. Gabriel. Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate. J. Funct. Anal., Vol.272, No.8 (2017), pp.3455-3485.

[15] M. Chyba, J.-M. Coron, P. Gabriel, Y. Mileyko, and H. Rezaei. Identification of the fragmentation role in the amyloid assembling processes and application to their optimization. Proceedings of the SIAM Conference on Control and its Applications (CT15), Paris, 2015, pp.348-355.

[14] P. Gabriel. Global stability for the prion equation with general incidence. Math. Biosc. Eng., Special issue dedicated to the 70th birthday of Glenn F. Webb, Vol.12, No.4 (2015), pp.789-801.

[13] M. Chyba, J.-M. Coron, P. Gabriel, A. Jacquemard, G. Patterson, G. Picot, and P. Shang. Optimal geometric control applied to the Protein Misfolding Cyclic Amplification process. Acta Appl. Math., Special Issue Control and Observation of Nonlinear Control Systems with Applications to Medicine and Space Mechanics, Vol.135, No.1 (2015), pp.145-173.

[12] V. Calvez, P. Gabriel, and S. Gaubert. Non-linear eigenvalue problems arising from growth maximization of positive linear dynamical systems. Proceedings of the 53rd IEEE Annual Conference on Decision and Control (CDC), Los Angeles, CA, 2014, pp.1600-1607.

[11] J.-M. Coron, P. Gabriel, and P. Shang. Optimization of an amplification protocol for misfolded proteins by using relaxed control. J. Math. Biol., Vol.70, No.1-2 (2015), pp.289-327.

[10] P. Gabriel and F. Salvarani. Exponential relaxation to self-similarity for the superquadratic fragmentation equation. Appl. Math. Lett., Vol.27 (2014), pp.74-78.

[9] D. Balagué, J. A. Cañizo, and P. Gabriel. Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates. Kinetic Related Models, Vol.6, No.2 (2013), pp.219-243.

[8] V. Calvez and P. Gabriel. Optimal growth for linear processes with affine control. arXiv:1203.5189 (2012).

[7] S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel, L. M. Tine, H. Rezaei, and M. Doumic. An efficient kinetic model for amyloid fibrils assemblies and its application to polyglutamine aggregation. PLoS ONE, Vol.7, No.11 (2012), e43273.

[6] P. Gabriel, S. P. Garbett, V. Quaranta, D. R. Tyson, and G. F. Webb. The contribution of age structure to cell population responses to targeted therapeutics. J. Theor. Biol., Vol.311 (2012), pp.19-27.

[5] P. Gabriel. Long-time asymptotics for nonlinear growth-fragmentation equations. Comm. Math. Sci., Vol.10, No.3 (2012), pp.787-820.

[4] V. Calvez, M. Doumic, and P. Gabriel. Self-similarity in a general aggregation-fragmentation problem ; application to fitness analysis. J. Math. Pures Appl., Vol.98, No.1 (2012), pp.1-27.

[3] P. Gabriel. The shape of the polymerization rate in the prion equation. Math. Comput. Modelling, Special Issue Mathematical Methods and Modelling of Biophysical Phenomena, Vol.53, No.7-8 (2011), pp.1451-1456.

[2] P. Gabriel and L. M. Tine. High-order WENO scheme for polymerization-type equations. ESAIM Proc., CEMRACS 2009: Mathematical Modelling in Medicine, Vol.30 (2010), pp.53-69.

[1] M. Doumic and P. Gabriel. Eigenelements of a general aggregation-fragmentation model. Math. Models Methods Appl. Sci., Vol.20, No.5 (2010), pp.757-783.

Dissertations

Habilitation thesis: Asymptotic analysis of non-local equations arising in biology (January 2021)

PhD thesis: Transport-fragmentation equations and applications to prion diseases (June 2011)