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Pierre Gabriel

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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, 28 (12), pp.5905--5933. ⟨10.3934/dcdsb.2022120⟩
Journal articles hal-03376957v2
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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⟩
Journal articles hal-02062882v3
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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⟩
Journal articles hal-02290410v3
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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⟩
Journal articles hal-02973959v2
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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⟩
Journal articles hal-01883140v3
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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⟩
Journal articles hal-01617088v4
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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⟩
Journal articles hal-01617071v4
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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⟩
Journal articles hal-02291295v2
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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⟩
Journal articles hal-01742140v1
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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⟩
Journal articles hal-01372949v2
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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⟩
Journal articles hal-01363549v5
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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⟩
Journal articles hal-01500471v2
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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⟩
Journal articles hal-01313817v3
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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⟩
Journal articles hal-01002824v2
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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⟩
Journal articles hal-00860218v2

Optimal Geometric Control Applied to the Protein Misfolding Cyclic Amplification Process

Monique Chyba , Jean-Michel Coron , Pierre Gabriel , Alain Jacquemard , Geoffrey Patterson
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⟩
Journal articles hal-01313871v1
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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⟩
Journal articles hal-00860231v4
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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⟩
Journal articles hal-00683148v2
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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⟩
Journal articles hal-00539279v2
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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⟩
Journal articles hal-00649178v2
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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⟩
Journal articles hal-00565863v2
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An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation.

Stephanie Prigent , Annabelle Ballesta , Frédérique Charles , Natacha Lenuzza , Pierre Gabriel
PLoS ONE, 2012, 7 (11), pp.e43273. ⟨10.1371/journal.pone.0043273⟩
Journal articles hal-00778052v1
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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⟩
Journal articles hal-00455390v2
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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⟩
Journal articles hal-00408088v3
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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⟩
Journal articles hal-00455472v2
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Équations de transport-fragmentation et applications aux maladies à prions

Pierre Gabriel
Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2011. Français. ⟨NNT : ⟩
Theses tel-00635281v1
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Asymptotic analysis of non-local equations arising in biology

Pierre Gabriel
Mathematics [math]. Université Paris-Saclay, Université Versailles Saint-Quentin-en-Yvelines, 2021
Habilitation à diriger des recherches tel-03144625v1