Ouvrages individuels et direction d’ouvrages collectifs

[Ed5]	K. Ammari, A. Doubouva, S. Gerbi and M. González-Burgos Advances on Partial Differential Equations and Control, Trends in Mathematics, Birkhäuser Cham, August 2024, 250 pages. [doi]
[Ed4]	K. Ammari and S. Gerbi Identification and Control: Some New Challenges, Contemporary Mathematics, Volume 757, American Mathematical Society, Novembre 2020, 191 pages. [ConM-AMS]
[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]
[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]
[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

[33]	Z. Abdallah, S. Gerbi, C. Kassem and A. Wehbe, Stability for an interface transmission problem of wave-plate equations with dynamical boundary controls, Acta Applicandae Mathematicae, Vol. 188, No 1, article 12 (2023), 38 pages [doi] [HAL] [arXiv]
[32]	R. Lteif and S. Gerbi, A new class of higher-ordered/extended Boussinesq system for efficient numerical simulations by splitting, Applied Mathematics and Computation, Vol. 432, 1st November 2022, article 127373, (2022), 30 pages [doi] [HAL] [arXiv]
[31]	S. Gerbi, C. Kassem and A. Wehbe, Polynomial stabilization of non-smooth direct/indirect elastic/viscoelastic damping problem involving Bresse system, ZAMP-Zeitschrift für Angewandte Mathematik und Physik, Journal of Applied Mathematics and Physics, Volume 73, No 3, article 89, (2022), 32 pages [doi] [HAL] [arXiv]
[30]	B. Khorbatly, R. Lteif, S. Israwi and S. Gerbi, Mathematical modeling and numerical analysis for the higher order Boussinesq system, ESAIM: M2AN, Mathematical Modelling and Numerical Analysis, Volume 56, No 2, (2022), pp. 593–615. [doi] [HAL] [arXiv]
[29]	S. Gerbi, C. Kassem, A. Mortada and A. Wehbe Numerical study of the stabilization of 1D locally coupled wave equations, ZAA-Zeitschrift für Analysis und ihre Anwendungen, Journal of Analysis and Its Applications, Volume 40, Issue 2, (2021), pp. 131–151. [doi] [HAL] [arXiv]
[28]	S. Gerbi, C. Kassem, A. Mortada and A. Wehbe Exact controllability and stabilization of locally coupled wave equations : theoretical results, ZAA-Zeitschrift für Analysis und ihre Anwendungen, Journal of Analysis and Its Applications, Volume 40, Issue 1, (2021), pp. 67–96. [doi] [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), pp. 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, Journal of Analysis and Its Applications, 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. [doi] [HAL] [arXiv]
[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. [doi] [HAL] [arXiv]
[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. [doi] [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

[C15]	Z. Abdallah, S. Gerbi and A. Wehbe Energy decay estimate for a wave-plate interface transmission problem with only two dynamical boundary controls, in Advances on Partial Differential Equations and Control, A. Doubova, K. Ammari, S. Gerbi and M. Gonzalez-Burgos (Eds), Trends in Mathematics, Birkhäuser Cham, (2024), pp. 3-36. [doi]
[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), pp 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), pp. 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), pp. 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), pp. 207-214. [doi] [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), pp. 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), pp. 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), pp. 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), pp. 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.