Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS
UFC
CNRS


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English version

Current position

I am currently Lecturer and Associate Professor at the University of Franche-Comté - Laboratory of Mathematics


Research topics



Numerical methods

  • Finite volume methods for hyperbolic conservation laws

  • Reduced basis methods the rapid resolution of PDE

  • Implementation of numerical schemes and numerical simulations

Mathematical analysis of partial differential equations

  • Partial differential equations in unbounded domains

  • Functional properties of weighted Sobolev spaces

Domains of application


Fluid Mechanics

  • Viscous and incompressible fluid flows in unbounded domains (Navier-Stokes, Oseen and Stokes equations)

  • Shallow water flows (Saint-Venant equations)

  • Trafic flow (Lighthill-Whitham-Richards, Aw-Rascle-Zhang type models)

Biology

  • Epidemiology models, prey-predator models

  • Evolution of transposable elements in the genome

Scientific publications



Submitted papers


[1] B. Andreianov, C. Donadello, U. Razafison, M. D. Rosini
Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux
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Published or accepted articles


[18] B. Andreianov, C. Donadello, U. Razafison, M. D. Rosini
Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local constraints on the flux and modeling of crowd dynamics at the bottlenecks
ESAIM Math. Model. Numer. Anal., 50 (2016) no. 5, 1269—1287.
Link to the publication
PDF

[17] H. Louati, M. Meslameni, U. Razafison
Weighted $L^p$ theory for vector potential operators in three-dimensional exterior domains
Math. Method Appl. Sci., 39 (2016) no. 8, 1990—2010.
Link to the publication
PDF

[16] V. Milisic, U. Razafison
Weighted $L^p$-theory for Poisson, biharmonic and Stokes problems on periodic unbounded strips of $\mathbb{R}^n$
Ann. Univ. Ferrara Sez. VII Sci. Mat., 62 (2016) no. 1, 117—142.

Link to the publication
PDF

[15] A. Perasso, U. Razafison
Identifiability problem for recovering the mortality rate in an age-structured population dynamics model
Inverse Probl. Sci. Eng. 24 (2016) no. 4, 711—728.
Link to the publication
PDF

[14] B. Andreianov, C. Donadello, U. Razafison, J. Y. Rolland, M. D. Rosini
Solutions of the Aw-Rascle-Zhang system with point constraints
Netw. Heterog. Media, 11 (2016) no. 1, 29—47.
Link to the publication
PDF sur HAL

[13] B. Andreianov, C. Donadello, S. S. Ghoshal, U. Razafison
On the attainable set for a class of triangular systems of conservation laws
J. Evol. Equ. 15 (2015), no. 3, 503—532
Link to the publication
PDF

[12] B. Andreianov, C. Donadello, U. Razafison, M. D. Rosini
Riemann problems with non-local point constraints and capacity drop
Math. Biosci. Eng. 12 (2015), no. 2, 259—278.
Link to the publication
PDF

[11] A. Perasso, U. Razafison
Asymptotic behavior and numerical simulations for an infection load-structured epidemiological models ; Application to the transmission of prion pathologies
SIAM J. Appl. Math. 74 (2014), no. 5, 1571—1597.
Link to the publication
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[10] U. Razafison, S. Cordier, O. Delestre, F. Darboux, C. Lucas, F. James
A Shallow Water model for the numerical simulation of overland flow on surfaces with ridges and furrows
Eur. J. Mech. B Fluids. 31 (2012), 44—52.
Link to the publication
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[9] C. Amrouche, H. Bouzit, U. Razafison
On the two and three dimensional Oseen potentials
Potential Anal. 34 (2011), no. 2, 163—179.
Link to the publication
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[8] V. de la Rubia, U. Razafison, Y. Maday
Reliable Fast Frequency Sweep for Microwave Devices via the Reduced Basis Method
IEEE Trans. Microwave Theory Tech. 57 (2009), no. 12 (1), 2923—2937.
Link to the publication
PDF

[7] U. Razafison
The stationary Navier-Stokes equations in 3D exterior domains. An approach in anisotropically weighted $L^q$ spaces
J. Differential Equations 245 (2008), 2785—2801.
Link to the publication
PDF

[6] C. Amrouche, U. Razafison
The stationary Oseen equations in $\mathbb{R}^3$. An approach in weighted Sobolev spaces
J. Math. Fluid Mech.9 (2007), no. 2, 211—225.
Link to the publication.

[5] C. Amrouche, U. Razafison
Weighted Sobolev spaces for a scalar model of the stationary Oseen equations in $\mathbb{R}^3$
J. Math. Fluid Mech. 9 (2007), no. 2, 181—210.
Link to the publication

[4] U. Razafison
Anisotropic weighted $L^p$ spaces for the stationary exterior 3D problem of Oseen
J. Math. Anal. Appl. 323 (2006), no. 1, 275—292.
Link to the article

[3] C. Amrouche, U. Razafison
On the Oseen problem in three dimensional exterior domains
Anal. Appl. (Singap.) 4 (2006), no. 2, 133—162.
Link to the publication.

[2] C. Amrouche, U. Razafison
Anisotropically weighted Poincaré-type inequalities ; Application to the Oseen problem
Math. Nachr. 279 (2006), no. 9—10, 931—947.
Link to the publication.

[1] T. Z. Boulmezaoud, U. Razafison
On the steady Oseen problem in the whole space
Hiroshima Math. J. 35 (2005), no. 3, 371—401.
Link to the publication

 

Notes and Comptes Rendus de l’Académie des Sciences

 

[5] S. Del Pino, U. Razafison, D. Yakoubi
Une borne inférieure pour la constante de la condition inf-sup sur l’opérateur de divergence
C. R. Acad. Sci. Paris. Ser. I, 346 (2008), no. 9—10, 533—538.
Link to the publication
PDF

[4] Y. Maday, U. Razafison
A reduced basis method applied to the Restricted Hartree-Fock equations
C. R. Acad. Sci. Paris, Ser. I, 346 (2008), no. 3—4, 243—248.
Link to the publication

[3] C. Amrouche, U. Razafison
Weighted estimates for the Oseen problem in $\mathbb{R}^3$
Appl. Math. Lett. 19 (2006), no. 1, 56—62.
Link to the publication

[2] C. Amrouche, U. Razafison
On the existence of solutions in weighted Sobolev spaces for the exterior Oseen problem
C. R. Acad. Sci. Paris, ser. I, 341 (2005), no. 9, 587—592.
Link to the publication

[1] C. Amrouche, U. Razafison
Espaces de Sobolev avec poids et équation scalaire d’Oseen dans $\mathbb{R}^n$
C. R. Acad. Sci. Paris, ser. I, 337 (2003), no. 12, 761—766.
Link to the publication

 

Proceedings

 

[5] O. Delestre, U. Razafison
Numerical scheme for a viscous shallow water system including new friction laws of second order : validation and application
SimHydro 2014 : Modelling of rapid transitory flows, 11-13 June 2014, Sophia Antipolis.
PDF

[4] A. Perasso, U. Razafison
Infection load structured SI model with exponential velocity and external source of contamination
Proceedings of the World Congress on Engineering, Vol. I (2013), 263—267.
Link to the publication
PDF

[3] C. Amrouche, U. Razafison
Isotropic and anisotropic weighted Sobolev spaces for the Oseen equations
Advances in mathematical fluid mechanics, Springer, Berlin (2010), 1—24.

[2] C. Amrouche, U. Razafison
The Oseen equations in $\mathbb{R}^n$ and weighted Sobolev spaces
Monografias del Seminario Matematico Garcia de Galdeano, 31 (2004), 41—49.

[1] C. Amrouche, U. Razafison
Study of the scalar Oseen equation
Monografias del Seminario Matematico Garcia de Galdeano, 27 (2003), 57—64.

 

Habilitation à diriger des recherches

 

Habilitation à diriger des recherches defended on December 3, 2015 at the Université de Franche-Comté
Contribution à l’analyse théorique de problèmes elliptiques en domaine non borné, à la simulation numérique d’équations hyperboliques et aux méthodes de bases réduites
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Ph. D. Thesis

 

Ph. D. thesis under the supervision of Chérif Amrouche defended July 1, 2004 at the Université de Pau et des Pays de l’Adour
Théorie $L^p$ avec poids pour les équations d’Oseen dans des domaines non bornés
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