Ouvrages scientifiques

[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. [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

[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, 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, 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 , 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, 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 , 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, 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 , 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 , 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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

[C12] C. Demay, C. Bourdarias, B. de Laage de Meux,S. Gerbi, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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

[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, 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, 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, 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, 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.