Pierre Gabriel

37
Documents
Affiliations actuelles
  • Université de Tours (UT)
  • Institut Denis Poisson (IDP)

Publications

Publications

Image document

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-03608758 v2
Image document

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-03376957 v2
Image document

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-02062882 v3
Image document

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-02290410 v3
Image document

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-02973959 v2
Image document

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-01617088 v4
Image document

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-01617071 v4
Image document

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-01883140 v3
Image document

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-02291295 v2
Image document

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-01363549 v5
Image document

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-01372949 v2
Image document

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-01742140 v1
Image document

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-01500471 v2
Image document

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-01313817 v3
Image document

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-00860218 v2

Optimal Geometric Control Applied to the Protein Misfolding Cyclic Amplification Process

Monique Chyba , Jean-Michel Coron , Pierre Gabriel , Alain Jacquemard , Geoffrey Patterson et 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-01313871 v1
Image document

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-01002824 v2
Image document

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-00860231 v4
Image document

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-00683148 v2
Image document

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-00649178 v2
Image document

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-00539279 v2
Image document

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 et al.
PLoS ONE, 2012, 7 (11), pp.e43273. ⟨10.1371/journal.pone.0043273⟩
Article dans une revue hal-00778052 v1
Image document

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-00565863 v2
Image document

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-00455390 v2
Image document

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-00408088 v3
Image document

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-00455472 v2
Image document

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-00635281 v1
Image document

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-03144625 v1