Pierre Gabriel

Publications

Article dans une revue (26)

Fast, slow convergence, and concentration in the house of cards replicator-mutator model Bertrand Cloez,Pierre Gabriel Differential and integral equations, 2024, 37 (7-8), pp.547-584. ⟨10.57262/die037-0708-547⟩ Article dans une revue hal-03608758v2
Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics Matthieu Alfaro,Pierre Gabriel,Otared Kavian Discrete and Continuous Dynamical Systems - Series B, 2023, Special issue in memory of Masayasu Mimura, 28 (12), pp.5905--5933. ⟨10.3934/dcdsb.2022120⟩ Article dans une revue hal-03376957v2
A Non-Conservative Harris Ergodic Theorem Vincent Bansaye,Bertrand Cloez,Pierre Gabriel,Aline Marguet Journal of the London Mathematical Society, 2022, 106 (3), pp.2459-2510. ⟨10.1112/jlms.12639⟩ Article dans une revue hal-02062882v3
Periodic asymptotic dynamics of the measure solutions to an equal mitosis equation Pierre Gabriel,Hugo Martin Annales Henri Lebesgue, 2022, 5, pp.275-301. ⟨10.5802/ahl.123⟩ Article dans une revue hal-02290410v3
Spectral gap for the growth-fragmentation equation via Harris's Theorem José A. Cañizo,Pierre Gabriel,Havva Yoldaş SIAM Journal on Mathematical Analysis, 2021, 53 (5), pp.5185-5214. ⟨10.1137/20M1338654⟩ Article dans une revue hal-02973959v2
Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions Vincent Bansaye,Bertrand Cloez,Pierre Gabriel Acta Applicandae Mathematicae, 2020, 166 (1), pp.29-72. ⟨10.1007/s10440-019-00253-5⟩ Article dans une revue hal-01617071v4
The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states Grégory Dumont,Pierre Gabriel Nonlinearity, 2020, 33 (12), pp.6381-6420. ⟨10.1088/1361-6544/aba6d8⟩ Article dans une revue hal-01617088v4
Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate Etienne Bernard,Pierre Gabriel Journal of Evolution Equations, 2020, 20 (2), pp.375-401. ⟨10.1007/s00028-019-00526-4⟩ Article dans une revue hal-01883140v3
On an irreducibility type condition for the ergodicity of nonconservative semigroups Bertrand Cloez,Pierre Gabriel Comptes Rendus. Mathématique, 2020, 358 (6), pp.733-742. ⟨10.5802/crmath.92⟩ Article dans une revue hal-02291295v2
Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts Etienne Bernard,Marie Doumic,Pierre Gabriel Kinetic and Related Models , 2019, 12 (3), pp.551-571. ⟨10.3934/krm.2019022⟩ Article dans une revue hal-01363549v5
Steady distribution of the incremental model for bacteria proliferation Pierre Gabriel,Hugo Martin Networks and Heterogeneous Media, 2019, Special issue on mathematical methods in systems biology, 14 (1), pp.149-171. ⟨10.3934/nhm.2019008⟩ Article dans une revue hal-01742140v1
Limiting Hamilton-Jacobi equation for the large scale asymptotics of a subdiffusion jump-renewal equation Vincent Calvez,Pierre Gabriel,Álvaro Mateos González Asymptotic Analysis, 2019, 115 (1-2), pp.63-94. ⟨10.3233/ASY-191528⟩ Article dans une revue hal-01372949v2
Measure solutions to the conservative renewal equation Pierre Gabriel ESAIM: Proceedings and Surveys, 2018, CIMPA School on Mathematical Models in Biology and Medicine, 62, pp.68-78. ⟨10.1051/proc/201862186206⟩ Article dans une revue hal-01500471v2
Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate Etienne Bernard,Pierre Gabriel Journal of Functional Analysis, 2017, 272 (8), pp.3455-3485. ⟨10.1016/j.jfa.2017.01.009⟩ Article dans une revue hal-01313817v3
Optimization of an Amplification Protocol for Misfolded Proteins by using Relaxed Control Jean-Michel Coron,Pierre Gabriel,Peipei Shang Journal of Mathematical Biology, 2015, 70 (1), pp.289-327. ⟨10.1007/s00285-014-0768-9⟩ Article dans une revue hal-00860218v2
Optimal Geometric Control Applied to the Protein Misfolding Cyclic Amplification Process Monique Chyba,Jean-Michel Coron,Pierre Gabriel,Alain Jacquemard,Geoffrey Pattersonet al. Acta Applicandae Mathematicae, 2015, Control and Observation of Nonlinear Control Systems with Applications to Medicine and Space Mechanics, 135 (1), pp.145-173. ⟨10.1007/s10440-014-9950-8⟩ Article dans une revue hal-01313871v1
Global stability for the prion equation with general incidence Pierre Gabriel Mathematical Biosciences and Engineering, 2015, Special issue dedicated to the 70th birthday of Glenn F. Webb, 12 (4), pp.789-801. ⟨10.3934/mbe.2015.12.789⟩ Article dans une revue hal-01002824v2
Exponential relaxation to self-similarity for the superquadratic fragmentation equation Pierre Gabriel,Francesco Salvarani Applied Mathematics Letters, 2014, 27, pp.74-78. ⟨10.1016/j.aml.2013.08.001⟩ Article dans une revue hal-00860231v4
Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates Daniel Balagué,José Cañizo,Pierre Gabriel Kinetic and Related Models , 2013, 6 (2), pp.219-243. ⟨10.3934/krm.2013.6.219⟩ Article dans une revue hal-00683148v2
An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation. Stephanie Prigent,Annabelle Ballesta,Frédérique Charles,Natacha Lenuzza,Pierre Gabrielet al. PLoS ONE, 2012, 7 (11), pp.e43273. ⟨10.1371/journal.pone.0043273⟩ Article dans une revue hal-00778052v1
The contribution of age structure to cell population responses to targeted therapeutics Pierre Gabriel,Shawn P. Garbett,Vito Quaranta,Darren R. Tyson,Glenn F. Webb Journal of Theoretical Biology, 2012, 311, pp.19-27. ⟨10.1016/j.jtbi.2012.07.001⟩ Article dans une revue hal-00649178v2
Self-similarity in a General Aggregation-Fragmentation Problem ; Application to Fitness Analysis Vincent Calvez,Marie Doumic-Jauffret,Pierre Gabriel Journal de Mathématiques Pures et Appliquées, 2012, 98 (1), pp.1-27. ⟨10.1016/j.matpur.2012.01.004⟩ Article dans une revue hal-00539279v2
Long-time Asymptotics for Nonlinear Growth-fragmentation Equations Pierre Gabriel Communications in Mathematical Sciences, 2012, 10 (3), pp.787-820. ⟨10.4310/CMS.2012.v10.n3.a4⟩ Article dans une revue hal-00565863v2
The Shape of the Polymerization Rate in the Prion Equation Pierre Gabriel Mathematical and Computer Modelling, 2011, Mathematical Methods and Modelling of Biophysical Phenomena, 53 (7-8), pp.1451-1456. ⟨10.1016/j.mcm.2010.03.032⟩ Article dans une revue hal-00455390v2
High-order WENO scheme for Polymerization-type equations Pierre Gabriel,Léon Matar Tine ESAIM: Proceedings and Surveys, 2010, CEMRACS 2009: Mathematical Modelling in Medicine, 30, pp.53-69. ⟨10.1051/proc/2010006⟩ Article dans une revue hal-00455472v2
Eigenelements of a General Aggregation-Fragmentation Model Marie Doumic-Jauffret,Pierre Gabriel Mathematical Models and Methods in Applied Sciences, 2010, 20 (5), pp.757-783. ⟨10.1142/S021820251000443X⟩ Article dans une revue hal-00408088v3

Communication dans un congrès (2)

Identification of the Fragmentation Role in the Amyloid Assembling Processes and Application to their Optimization Monique Chyba,Jean-Michel Coron,Pierre Gabriel,Yuriy Mileyko,Human Rezaei SIAM Conference on Control and its Applications, Jul 2015, Paris, France. pp.348--355, ⟨10.1137/1.9781611974072.48⟩ Communication dans un congrès hal-01313887v1
Non-linear eigenvalue problems arising from growth maximization of positive linear dynamical systems Vincent Calvez,Pierre Gabriel,Stéphane Gaubert IEEE 53rd Annual Conference on Decision and Control (CDC 2014), Dec 2014, Los Angeles, United States. pp.1600--1607, ⟨10.1109/CDC.2014.7039628⟩ Communication dans un congrès hal-00974749v1

Pré-publication, Document de travail (6)

Subdiffusive fractional limit of a jump-renewal equation Hugues Berry,Pierre Gabriel,Thomas Lepoutre,Nathan Quiblier 2026 Pré-publication, Document de travail hal-05456904v1
On the Krein-Rutman theorem and beyond Claudia Fonte Sánchez,Pierre Gabriel,Stéphane Mischler 2025 Pré-publication, Document de travail (preprint/prepublication) hal-04093201v3
Constructive Krein-Rutman result for Kinetic Fokker-Planck equations in a domain Kleber Carrapatoso,Pierre Gabriel,Richard Medina,Stéphane Mischler 2024 Pré-publication, Document de travail hal-04650292v2
Spectral description of a cell growth and division equation Pierre Gabriel,Bruce van Brunt,Graeme Charles Wake,Ali Ashher Zaidi 2024 Pré-publication, Document de travail hal-04707890v1
The principal eigenvalue problem for time-periodic nonlocal equations with drift Bertrand Cloez,Adil El Abdouni,Pierre Gabriel 2024 Pré-publication, Document de travail hal-04690839v1
Optimal growth for linear processes with affine control Vincent Calvez,Pierre Gabriel 2012 Pré-publication, Document de travail hal-00681920v1

Thèse (1)

Équations de transport-fragmentation et applications aux maladies à prions Pierre Gabriel Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2011. Français. ⟨NNT : ⟩ Thèse tel-00635281v1

HDR (1)

Asymptotic analysis of non-local equations arising in biology Pierre Gabriel Mathematics [math]. Université Paris-Saclay, Université Versailles Saint-Quentin-en-Yvelines, 2021 HDR tel-03144625v1

Cours (2)

Measure solutions to the conservative renewal equation Pierre Gabriel Doctoral. Moka, Mauritius. 2016, pp.12 Cours cel-01499728v2
Équations structurées en dynamique des populations Pierre Gabriel Licence. ENS Cachan, France. 2014, pp.20 Cours cel-00918869v2