Prépublication/Preprint

33. Diffusion-approximation of a kinetic equation with stochastically perturbed velocity redistribution process, Nils Caillerie, Julien Vovelle
32. Diffusion-approximation in stochastically forced kinetic equations, Arnaud Debussche, Julien Vovelle
31. Convergence of the Finite Volume Method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation, Sylvain Dotti, Julien Vovelle

 
Divers/Various works

Stochastic scalar first-order conservation laws, Course given at TIFR-CAM, Bangalore, May 2018.
Scalar conservation laws with stochastic forcing, revised version, A. Debussche, J. Vovelle
Stochastic perturbation of scalar conservation laws, Course given at the Spring School Analytical and Numerical Aspects of Evolution Equations T.U. Berlin, April 2009.
Mémoire d'habilitation à diriger des recherches, Décembre 2011

 
Publications

2018
30. Convergence of approximations to stochastic scalar conservation laws, Archive for Rational Mechanics and Analysis, (), 1-53, 2018, Sylvain Dotti, Julien Vovelle
2017
29. Stochastic isentropic Euler equations, to appear in Annales de l'ENS, F. Berthelin, J. Vovelle
28. Invariant Measures for a Stochastic Fokker-Planck Equation, to appear in Kinetic and Related Models (KRM), S. De Moor, M. Rodrigues, J. Vovelle
27. Regularity of Stochastic Kinetic Equations, Electron. J. Probab. Volume 22 (2017), paper no. 48, 42 pp, Ennio Fedrizzi, Franco Flandoli, Enrico Priola, Julien Vovelle
2016
26. Diffusion limit for the radiative transfer equation perturbed by a Markov process, Asymptotic Analysis, 2016, 98 (1-2), pp.31-58, A. Debussche, S. De Moor, J. Vovelle
2015
25. Diffusion limit for the radiative transfer equation perturbed by a Wiener process, Kinetic and Related Models, Volume 8, Issue 3, 2015 Pages 467-492, A. Debussche, S. De Moor, J. Vovelle
24. Degenerate parabolic stochastic partial differential equations: quasilinear case, The Annals of Probability, 2016, 44 (3), pp.1916-1955, A. Debussche, M. Hofmanová, J. Vovelle
23. Invariant measure of scalar first-order conservation laws with stochastic forcing, Probability Theory and Related Fields: Volume 163, Issue 3 (2015), Page 575-611, A. Debussche, J. Vovelle
2012
22. A kinetic approach in nonlinear parabolic problems with L1-data, ZAA, Volume 31, Issue 3, 2012, pp 307-334, M. Pierre, J. Vovelle
21. On a phase field model for solid-liquid phase transitions, Discrete and Continuous Dynamical System-A, Volume 32, Issue 6, 2012, Pages 1997-2025, S. Benzoni-Gavage, L. Chupin, D. Jamet, J. Vovelle
20. Diffusion limit for a stochastic kinetic problem, Communications on Pure and Applied Analysis, Volume 11, Issue 6, November 2012, Pages: 2305 - 2326, A. Debussche, J. Vovelle
2010
19. Existence and regularity of extremal solutions for a mean-curvature equation, J. Differential Equations 249 (2010), 37-75, A. Mellet, J. Vovelle
18. Scalar conservation laws with stochastic forcing, J. Funct. Anal. (2010), doi:10.1016/j.jfa.2010.02.016, A. Debussche, J. Vovelle
17. A BGK approximation to scalar conservation laws with discontinuous flux, Proceedings A of the Royal Society of Edinburgh, 140, no. 5, (2010), pp 953 -- 972, F. Berthelin, J. Vovelle
2009
16. Long-time behavior in scalar conservation laws, Differential and Integral Equations, 22 (2009), no. 3-4, 225-238, A. Debussche, J. Vovelle
2008
15. Convergence of the Finite Volume Method for scalar conservation laws with discontinuous flux function, M2AN Math. Model. Numer. Anal. 42 (2008), no. 5, 699--727, S. Martin, J. Vovelle
2007
14. About Global Existence for Quadratic Systems of Reaction-Diffusion, Advanced Nonlinear Studies, 7 (2007), no. 3, 491--511, L. Desvillettes, K. Fellner, M. Pierre, J. Vovelle
13. Large-time behaviour of the entropy solution of a scalar conservation law with boundary conditions, Quart. J. of Mech. and Appl. Maths., 65 (2007), no. 3, 425--450, S. Martin, J. Vovelle
12. Occurence and non-appearance of shocks in fractal Burgers equations, Journal of Hyperbolic Differential Equations, 4 (2007), no. 3, 479--499, N. Alibaud, J. Droniou, J. Vovelle
11. Error estimate for the finite volume scheme applied to the advection equation, Numerische Mathematik 106 (2007), no. 1, 129--155, B. Merlet, J. Vovelle
2006
10. Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients, Comm. Partial Differential Equations, 31 (2006), pp.~371--395, F. Bachmann, J. Vovelle
9. Error estimates for the approximation of non-linear conservation laws on bounded domains by the finite volume method, Math. Comp., 75 (2006), pp.~113--150, M. Ohlberger, J. Vovelle
2004
8. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (2004), no.~5, 689--714, J. Droniou, C. Imbert, J. Vovelle
7. Kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications, SIAM J. Math. Anal. 36 (2004), no.~1, 214--232, C. Imbert, J. Vovelle
2003
6. Limit boundary conditions for finite volume approximations of some physical problems, Journal of Computational and Applied Mathematics (2003), Vol 161, pp 349-369, R. Eymard, T. Gallouet, J. Vovelle
5. Global solution and smoothing effect for a non-local regularization of an hyperbolic equation, Journal of Evolution Equations, Vol. P. Bénilan (2003) vol 3, no 3, pp 499-521, J. Droniou, T. Gallouet, J. Vovelle
4. Entropy Formulation for Parabolic Degenerate Equations with General Dirichlet Boundary Conditions and Application to the Convergence of FV Methods , SIAM Journal of numerical analysis, (2003), vol 41, no 6, pp 2262-2293, A. Michel, J. Vovelle
3. Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficient, M3AS, 13 (2003), no 2, pp 221-257, N. Seguin, J. Vovelle
2. L1 solutions to first order hyperbolic equations in bounded domains, CPDE, 28 (2003), 1&2, pp 381-408, A. Porretta, J. Vovelle
2002
1. Convergence of Finite Volume Scheme for Conservation Law on Bounded Domain, Numerische Mathematik 90 (2002), no. 3, 563-596. J. Vovelle