Ouvrages individuels et direction d’ouvrages collectifs

[Ed3] K. Ammari and S. Gerbi
Trends in Control and Inverse Problems, AIMS Series on Differential Equations & Dynamical Systems, Volume 6, American Institute of Mathematical Sciences, Octobre 2018, 119 pages. [AIMS]
AIMS Volume 6
[Ed2] K. Ammari and S. Gerbi
Evolution Equations: Long Time Behavior and Control, London Mathematical Society, Lecture Note Series, Volume 439, Cambridge University Press, Octobre 2017, 194 pages. [LMS]
LMS Volume 439
[Ed1] C. Bourdarias and S. Gerbi
Applied Mathematics In Savoie - AMIS 2012: Multiphase flow in industrial and environmental engineering, ESAIM Proceedings, Volume 40, July 2013, 143 pages. [ESAIM]

Articles publiés ou à paraître dans des revues internationales avec comité de lecture

[28] S. Gerbi, C. Kassem, A. Mortada and A. Wehbe
Exact controllability and stabilization of locally coupled wave equations à paraître dans ZAA-Zeitschrift für Analysis und ihre Anwendungen, 42 pages. [HAL] [arXiv]
[27] C. Demay, C. Bourdarias, B. de Laage de Meux, S. Gerbi and J-M Hérard
A splitting method adapted to the simulation of mixed flows in pipes with a compressible two-layer model, ESAIM: M2AN, Mathematical Modelling and Numerical Analysis, Volume 53, No 2, (2019), 405-442 [doi] [HAL]
[26] C. Demay, C. Bourdarias, B. de Laage de Meux, S. Gerbi and J-M Hérard
Numerical simulation of a compressible two-layer model: A first attempt with an implicit-explicit splitting scheme, Journal of Computational and Applied Mathematics, Volume 346, (2019), pp. 357–377. [doi] [HAL]
[25] C. Bourdarias S. Gerbi and R. Lteif
A numerical scheme for an improved Green–Naghdi model in the Camassa–Holm regime for the propagation of internal waves, Computers & Fluids, Volume 156, (2017), pp. 283-304. [doi] [HAL] [arXiv]
[24] K. Ammari and S. Gerbi
Interior feedback stabilization of wave equations with dynamic boundary delay, ZAA-Zeitschrift für Analysis und ihre Anwendungen, Volume 36, Issue 3, (2017), pp. 297–327. [doi] [HAL] [arXiv]
[23] C. Bourdarias, M. Ersoy and S. Gerbi
Unsteady flows in non uniform closed water pipes : a full kinetic approach, Numerische Mathematik, Vol. 128, No. 2, (2014), pp 217-263. [doi] [HAL] [arXiv]
[22] S. Gerbi and B. Said-Houari
Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions, Advances in Nonlinear Analysis, Vol. 2, No. 2, (2013), pp. 163-193. [doi] [HAL] [arXiv]
[21] C. Bourdarias, M. Ersoy and S. Gerbi
Air entrainment in transient flows in closed water pipes: a two-layer approach, ESAIM: M2AN, Mathematical Modelling and Numerical Analysis, Vol. 47, (2013), pp. 507-538. [doi] [HAL] [arXiv]
[20] S. Gerbi and B. Said-Houari
Existence and exponential stability of the damped wave equation with a dynamic boundary condition and a delay term, Applied Mathematics and Computation, Vol. 218, No. 24, (2012), pp. 11900-11910. [doi] [HAL] [arXiv]
[19] C. Bourdarias, M. Ersoy and S. Gerbi
A mathematical model for unsteady mixed flows in closed water pipes, Science China Mathematics, Vol. 55, No. 2, (2012), pp. 221-244. [doi] [HAL] [arXiv]
[18] S. Gerbi and B. Said-Houari
Exponential decay for solutions to semilinear damped wave equation, Discrete and Continuous Dynamical Systems, Series S, Vol. 5, No 3, (2012), pp. 559-566. [doi] [HAL] [arXiv]
[17] S. Gerbi and B. Said-Houari
Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions, Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, (2011), pp. 7137–7150. [doi] [HAL] [arXiv]
[16] C. Bourdarias, M. Ersoy and S. Gerbi
A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms, Journal of Scientific Computing, Vol. 48, No 1-3, (2011), pp. 89-104. [doi] [HAL] [arXiv]
[15] C. Bourdarias and S. Gerbi
A kinetic scheme for unsteady pressurised flows in closed water pipes, Journal of Computational and Applied Mathematics, Vol. 234, No 7, (2010), pp. 2098-2105. [doi] [HAL] [arXiv]
[14] C. Bourdarias, M. Ersoy and S. Gerbi
A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume, International Journal On Finite Volume, Vol. 6, No 2, (2009), pp 1-47. [HAL] [arXiv] [IJFV]
[13] C. Bourdarias, M. Ersoy and S. Gerbi
A kinetic scheme for pressurised flows in non uniform closed water pipes, Monografias de la Real Academia de Ciencias de Zaragoza, Vol. 31, (2009), pp. 1–20. [HAL] [arXiv] [pdf]
[12] C. Bourdarias, S. Gerbi and J. Ohayon
A pseudo active kinematic constraint for a biological living soft tissue: an effect of the collagen network, Mathematical and Computer Modelling, Vol. 49, No 11-12, (2009) pp. 2170-2181. [doi] [HAL] [arXiv]
[11] S. Gerbi and B. Said-Houari
Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions, Advances in Differential Equations, Vol. 13, No. 11-12, (2008), pp. 1051-1074. [HAL] [arXiv] [pdf]
[10] C. Bourdarias and S. Gerbi
A conservative model for unsteady flows in deformable closed pipes and its implicit second order finite volume discretisation, Computers and Fluids, Vol. 37, No 10, (2008), pp. 1225-1237. [doi] [pdf]
[9] C. Bourdarias, S. Gerbi and M. Gisclon
A kinetic formulation for a model coupling free surface and pressurised flows in closed pipes, Journal of Computational and Applied Mathematics, Vol. 218, No 2, (2008), pp. 522-531. [doi] [pdf]
[8] C. Bourdarias and S. Gerbi
A finite volume scheme for a model coupling unsteady flows in open channels and in pipelines, Journal of Computational and Applied Mathematics, Vol. 209, No 1, (2007), pp. 109-131. [doi] [pdf]
[7] J.P. Blais, L. Del Gatto, C. Bourdarias and S. Gerbi
Numerical modelling of mixed flows in hydroelectric schemes, La Houille Blanche, Vol. 1, (2006), pp. 76-81. [doi] [pdf]
[6] C. Bourdarias, S. Gerbi and J. Ohayon
A three dimensional finite element method for a biological active soft tissue. Formulation in cylindrical polar coordinates, ESAIM: M2AN, Mathematical Modelling and Numerical Analysis, Vol. 37, No 4, (2003), pp. 725-739. [doi] [pdf]
[5] V. Galaktionov, S. Gerbi and J.L. Vazquez
Quenching for a one dimensional fully nonlinear parabolic equation in detonation theory, SIAM J. Appl. Math., Vol. 61, No 4, (2000), pp. 1253-1285. [doi] [pdf]
[4] S. Gerbi, R. Herbin and E. Marchand
Existence of a solution to a coupled elliptic system with a Signorini's condition, Advances in Differential Equations, Vol. 4, No 2, (1999), pp. 225-251. [pdf]
[3] C.M. Brauner, S. Gerbi and Cl. Schmidt-Lainé
A stability analysis for a fully nonlinear problem in detonation theory, Applicable Analysis, Vol. 56, No 3-4, (1995), pp. 351-380. [doi] [pdf]
[2] P. Caussignac, S. Gerbi and L. Renggli
About admissible boundary conditions for Euler and parabolized Navier-Stokes equations, Helvetica Physica Acta, Vol. 63, No 5, (1990), pp. 607-615. [doi] [pdf]
[1] S. Gerbi, R. Herbin and V. Sonnad
Implementation of a parallel multigrid method on the experimental lCap supercomputer, Applied Mathematics and Computation, Vol. 27, No 4, (1988), pp. 281-312. [doi] [pdf]

Chapitre d'ouvrages et articles originaux dans des actes de conférence avec comité de lecture

[C14] C. Bourdarias , S. Gerbi and V. Winckler
Numerical Simulation of Mixed Flows in Hydroelectric Circuits with Temporary Flows Flowmix Software, in Advances in Hydroinformatics, Gourbesville P., Cunge J., Caignaert G. (Eds), Springer, Singapore, (2018), pp. 913-929. [doi] [pdf]
[C13] C. Bourdarias , S. Gerbi and V. Winckler
Latest developments of a mixed flows software in hydroelectric conduits with temporary flows (FlowMix), in Colloque CFBR-SHF : “Hydraulique des barrages et des digues”, Chambéry, 29 et 30 novembre 2017, Comité Français des Barrages et Réservoirs & Société Hydrotechnique de France, (2017), pp. 503-514. [doi] [pdf]
[C12] C. Demay, C. Bourdarias, B. de Laage de Meux, S. Gerbi and J-M Hérard
A Fractional Step Method to Simulate Mixed Flows in Pipes with a Compressible Two-Layer Model, in Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, Cancès, Clément and Omnes, Pascal, Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham, (2017), pp. 33-41. [doi] [pdf]
[C11] C. Bourdarias, S. Gerbi and R. Lteif
A Numerical Scheme for the Propagation of Internal Waves in an Oceanographic Model, in Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, Cancès, Clément and Omnes, Pascal, Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham, (2017), pp. 101-108. [doi] [pdf]
[C10] C. Bourdarias, S. Gerbi and J. Ohayon
Does the collagen network contributes to normal systolic left ventricular wall thickening ? A theoretical study in continuum mechanics, in Proceedings of the Second International Workshop on Functional Imaging and Modeling of the Heart, I. Magnin, J. Montagnat, P. Clarysse, J. Nenonen, and T. Katila (Eds.), Lecture Notes in Computer Science, vol. 2674, Springer, (2003), 91-100. [doi] [pdf]
[C9] C. Bourdarias, S. Gerbi and J. Ohayon
Loi de comportement du tissu myocardique tenant compte d'une contrainte cinématique induite par la matrice de collagène, 16éme Congrés Français de Mécanique,1-5 Septembre 2003, Nice, France, (CDROM), 6 pages, (2003). [pdf]
[C8] C. Bourdarias, S. Gerbi and J. Ohayon
A finite element method for the contraction analysis of the cardiac tissue: effect of the extracellular collagen network on the myocardial contraction, Proceedings of the 9th Workshop "The Finite Element Method in Biomedical Engineering, Biomechanics and Related Field", Ulm, Allemagne, (2002), 25-39. [pdf]
[C7] C. Bourdarias and S. Gerbi
An implicit finite volume scheme for unsteady flows in deformable pipe-lines, in Finite Volume for Complex Applications III, Problems and Perspectives, R. Herbin and D. Kröner (Eds.), (2002), 463-470. [pdf]
[C6] R. Cautrés, T. Gallouët, S. Gerbi and R. Herbin
A Neumann-Neumann method using a finite volume discretization, in Domain decomposition methods in science and engineering. Papers of the thirteenth international conference on domain decomposition methods, Lyon, France, October 9-12, 2000, N. Debit, M. Garbey, R. Hoppe, J. Périaux, D. Keyes, Y. Kuznetsov (Eds), International Center for Numerical Methods in Engineering (CIMNE). Theory Eng. Appl. Comput. Methods., Barcelona, (2002), 207-214. [pdf]
[C5] J. Ohayon, C. Bourdarias, S. Gerbi and C. Oddou
A three dimensional finite element method for a biological active soft tissue, ESAIM, Proc., 12, (2002), 8-11. [doi] [pdf]
[C4] J. Ohayon, C. Bourdarias, S. Gerbi and C. Oddou
A finite element for the active cardiac muscle, Proceedings of the Fifth International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, Rome, Italie, 2001, J. Middleton, N. G. Shrive, M. L. Jones (Eds.), (CDROM), 6 pages, (2001). [pdf]
[C3] V. Galaktionov,S. Gerbi, C. Schmidt-Lainé and J.-L. Vazquez
Bifurcation and quenching phenomena in an overdriven detonation model, EUROMECH 294, Theoretical Mechanics of Combustion, 1-4 Septembre 1992, Bristol, UK, (1992), 30-33.
[C2] S. Gerbi and G. Claus
An asymptotic model for detonation in duct, in Computational and Applied Mathematics II : Differential Equations, Selected and revised papers from the IMACS 13th world congress, Dublin, Ireland, July 1991, W.F. Ames and P.J. van der Houwen (Eds), North-Holland, (1992), 127-130.
[C1] S. Gerbi, R. Herbin and V. Sonnad
Parallel implementation of a multigrid method on a loosely coupled array of processors, in Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing, Los Angeles, California, USA, December 1-4, 1987, G. Rodrigue (Ed), SIAM, Philadelphia, (1989), 157-161.

Actes de congrés, rapports non publiés, thèse

[M10] C. Demay, C. Bourdarias, B. De Laage De Meux, S. Gerbi and J.-M. Hérard,
Splitting method and implicit-explicit schemes for a compressible gas-liquid model, Proceedings of ECCOMAS Congress 2016, VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete, Greece, June 5-10, (2016).
[M9] C. Demay, C. Bourdarias, B. De Laage De Meux, S. Gerbi and J.-M. Hérard,
A compressible two-layer model for transient two-phase flows in pipes, Proceedings of the WONAPDE 2016, Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations Universidad de Concepción, Concepción, Chile, January 11-15, (2016).
[M8] S. Gerbi
Etude mathématique et numérique de modèles en combustion, mécanique des fluides et biomécanique, HDR, Université de Savoie (2005).
[M7] C. Bourdarias and S. Gerbi
Etude et mise en oeuvre d'un schéma de type Roe pour les écoulements mixtes à surface libre et en charge. Rapport de validation, EDF-CIH, Décembre 2003.
[M6] C. Bourdarias and S. Gerbi
Etude et mise en oeuvre d'un schéma de type Roe pour les écoulements mixtes à surface libre et en charge. Rapport intermédiaire, EDF-CIH, Décembre 2001.
[M5] C. Bourdarias and S. Gerbi
A Finite Element Method for an Active Soft Tissue, First SIAM-EMS Conference Applied Mathematics in our Changing World, 2001, Berlin, Allemagne.
[M4] S. Gerbi
Etude mathématique d'une détonation en conduit, XXVéme Congrès National d'Analyse Numérique, 24-28 Mai 1993, Giens.
[M3] S. Gerbi
Etude mathématique d'un modèle de détonation en conduit, thèse de Doctorat, Université de Lyon I, 1993.
[M2] S. Gerbi
Sur les états stationnaires d'une détonation en conduit, XXIVème Congrès National d'Analyse Numérique, 25-28 Mai 1992, Vittel.
[M1] P. Caussignac, S. Gerbi, P. Leyland and L. Renggli,
Parabolized 2D Navier-Stokes equations : some results for linearized problems, Numerical Simulation in the Incompressible Case . A revised version, Rapport interne du DMA, EPF Lausanne, Janvier 1990.