## Publications and preprints

- [21] V. Bansaye, B. Cloez, and P. Gabriel. Ergodic behavior of non-conservative semigroups via generalized Doeblin's conditions.

*arXiv:1710.05584*, Oct. 2017.

- [20] G. Dumont and P. Gabriel. The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states.

*arXiv:1710.05596*, Oct. 2017.

- [19] P. Gabriel. Measure solutions to the conservative renewal equation. Submitted,

*arXiv:1704.00582*, Apr. 2017.

- [18] V. Calvez, P. Gabriel, and Á. Mateos González. Limiting Hamilton-Jacobi equation for the large scale asymptotics of a subdiffusion jump-renewal equation. Submitted,

*arXiv:1609.06933*, Sept. 2016.

- [17] É. Bernard, M. Doumic, and P. Gabriel. Cyclic asymptotic behaviour of a population reproducing by fission into two equal parts. Submitted,

*arXiv:1609.03846*, Sept. 2016.

- [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), p.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, p.348-355.

- [14] P. Gabriel. Global stability for the prion equation with general incidence.

*Math. Biosc. Eng.*, Vol.12, No.4 (2015), p.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.*, Vol.135 (2015), p.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, p.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), p.289-327.

- [10] P. Gabriel and F. Salvarani. Exponential relaxation to self-similarity for the superquadratic fragmentation equation.

*Appl. Math. Lett.*, Vol.27 (2014), p.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), p.219-243.

- [8] V. Calvez and P. Gabriel. Optimal growth for linear processes with affine control.

*arXiv:1203.5189 [math]*, Mar. 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), p.19-27.

- [5] P. Gabriel. Long-time asymptotics for nonlinear growth-fragmentation equations.

*Comm. Math. Sci.*, Vol.10, No.3 (2012), p.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), p.1-27.

- [3] P. Gabriel. The shape of the polymerization rate in the prion equation.

*Math. Comput. Modelling*, Vol.53, No.7-8 (2011), p.1451-1456.

- [2] P. Gabriel and L. M. Tine. High-order WENO scheme for polymerization-type equations.

*ESAIM Proc.*, Vol.30 (2010), p.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), p.757-783.

## Thesis

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