Systems of
conservation laws, I, Cambridge U. Press (1999), ISBN 0 521 58233 4.
Systems of
conservation laws, II, Cambridge U. Press (2000) ISBN 0 521 63330 3.
D. S.
Les Matrices : théorie et pratique, Masson (2001) ISBN
2 10 005515 1.
D. S.
Matrices : Theory and Applications, Grad. Text in Math.
216, Springer-Verlag (2002) ISBN 0 387 95460 0.
NEW ! The second edition has been released in November 2010.
The material is reorganised. The basics in linear and multilinear algebra
are given with more details.
New material includes.
See also the table of contents of the
1st edition,
the solutions of the exercises in
pdf (385 K) or in
postscript (480 K) formats,
an additional list
of 477 exercises (last update January 27th, 2020) in
pdf (3.7 MO) format. Illustrated with 32 stamps
from 19 different countries
the list of
errata (146 K),
a list of 8 (last update June 9th, 2006)
open problems.
S. Friedlander & D. S. Handbook of Mathematical Fluid Dynamics, Elsevier.
Volume I (2002, xi + 816 pages, ISBN 0 444 50330 7),
Volume II (2003, xi + 750 pages, ISBN 0 444 51287 X)
Volume III (2004, xi + 674 pages, ISBN 0 444 51556 9).
Volume IV (2007, xi + 711 pages, ISBN 0 444 52834 6).
S. Benzoni-Gavage & D. S.
Multi-dimensional hyperbolic partial differential equations. First order
systems and applications.
Oxford Mathematical Monographs,
Oxford University Press (2007, xxiv + 512 pages,
ISBN-10: 0-19-921123-X, ISBN 13: 978-0-19-921123-4).
To order.
D. S. Systems of conservation laws : A challenge for the XXIst century.
Mathematics Unlimited - 2001 and beyond, B. Engquist and W. Schmid
eds. Springer-Verlag (2001).
D. S. L1-stability of nonlinear waves in scalar conservation laws.
Handbook of Differential Equations.
Evolutionary Equations, vol. 1 . Eds: C. Dafermos,
E. Feireisl. Elsevier, North-Holland (2004), pp 473-553,
ISBN: 0-444-51131-8.
D. S. Discrete shock profiles: Existence and stability. CIME Summer
school in Cetraro, 14-21 July, 2003. P. Marcati editor.
Lecture Notes in Mathematics # 1911. Springer-Verlag (2007).
D. S. Shock reflection in gas dynamics.
Handbook of Mathematical Fluid Dynamics, vol. 4 . Eds:
S. Friedlander, D. Serre. Elsevier, North-Holland (2007). See the
errata
D. S.
Remarks about the discrete profiles of shock waves. Mathemática
Contemporânea, 11 (1996) pp 153-170.
D. S.
Solutions classiques globales des équations d'Euler pour un fluide
parfait compressible. Ann. Inst. Fourier, 47 (1997) pp
139-153.
M. Gisclon & D. S.
Conditions aux limites pour un système strictement hyperbolique fournies
par le schéma de Godunov. M2AN, 31
(1997) pp 359-380.
F. Hubert & D. S.
Dynamique lente-rapide pour des perturbations de systèmes de lois de
conservation, C.R.A.S. 322 (1996) pp 231-236.
F. Hubert & D. S.
Fast-slow dynamics for parabolic perturbations of conservation laws. SIAM
J. of Appl. Math. 21 (1996) pp 1587-1608.
H. Freistühler & D. S.
L1-stability of shock waves in scalar viscous conservation laws.
Comm. Pure Appl. Math. 51 (1998) pp 291-301.
Luo Tao & D. S.
Linear stability of shock profiles for a rate-type viscoelastic system with
relaxation. Quarterly of Appl. Math. LVI (1998) pp 569-586.
D. S.
Stabilité L1 pour des lois de conservation scalaires visqueuses.
C.R.A.S. 323 (1996) pp 359-363.
M. Bultelle, M. Grassin & D. S.
Unstable Godunov discrete profiles for steady shock waves. SIAM J. Num.
Anal. 35 (1998) pp 2272-2297.
Ling Hsiao & D. S.
Asymptotic behavior of large weak entropy solutions of the damped p-system.
J. Partial Diff. Eqs. 10 (1997) pp 355-368.
Ling Hsiao & D. S.
Global existence of solutions for the system of compressible adiabatic flow
through porous media.
SIAM J. Math. Anal. 27 (1996) pp 70--77.
M. Grassin & D. S. Existence de solutions globales et
régulières aux équations d'Euler pour un gaz parfait
isentropique. C.R.A.S. 325 (1997) pp 721-726.
D. S. Solutions globales (t<0 et t>0) des systèmes
paraboliques de lois de conservation. Ann. de l'Institut
Fourier 48 (1998) pp 1069-1091.
D. S. Discrete shock profiles and their stability. Hyperbolic problems
: Theory, Numerics, Applications. 7th International Conference, Zurich
1998. M. Fey, R. Jeltsch ed. ISNM 130 pp 843-854, Birkäuser (1999).
D. S. (Cet article a reçu le Prix des Annales de l'IHP 2000)
Relaxation semi-linéaire
et cinétique des systèmes de lois de
conservation. Ann. IHP, Anal. non-linéaire, 17 (2000),
pp 169-192.
H. Freistühler & D. S.
The L1-stability of boundary layers for scalar viscous conservation laws.
J. Dynamics and Diff. Eqns., 13 (2001) pp 145-155.
D. S. L1-decay and the stability of shock profiles.
PDEs. Theory and numerical solution.Prague, 1998. W. Jäger, J.
Necas, O. John, K. Najzar, J. Stará eds. Pitman
RNM 406 pp 312-321,
Chapman and Hall (1999).
C. Lattanzio & D.S.. Convergence of a relaxation scheme for
NxN hyperbolic systems of conservation laws. Numerische Mathematik,
88 (2001) pp 121-134.
C. Lattanzio & D.S.. Shock layers interactions for relaxation
approximation to conservation laws. No DEA Nonlinear Diff. Equ. and
Appl., 6 (1999) pp 319-340.
D.S.. La croissance de la vorticité dans les écoulements
parfaits incompressibles. C. R. A. S., 328 (1999) pp 549-552.
D.S.. La transition vers l'instabilité pour les ondes de choc
multi-dimensionnelles. Transactions of the A. M. S., 353 (2001) pp 5071-5093.
K. Zumbrun & D. S.. Viscous and inviscid stability of
multidimensional planar shock fronts. Indiana University Math.
Journal, 48 (1999) pp 937-992.
D.S.. Stabilité L1 d'ondes progressives de lois de conservation
scalaires. Séminaire EDPs de l'Ecole Polytechnique 1998-99.
S. Benzoni-Gavage,
D. S. &
K. Zumbrun, Alternate Evans functions
and viscous shock waves. SIAM J. Math. Anal., 32 (2001), pp
929-962.
D. S. Sur la stabilité des couches limites de viscosité.
Ann. de l'Institut
Fourier, 51 (2001) pp 109-129.
D. S. Stabilité L1 des chocs et de deux types de profils,
pour des lois de conservation scalaires. En
consultation.
D. S. &
K. Zumbrun, Boundary layer stability in real vanishing
viscosity limit. Communications in Math. Physics,
221 (2001) pp 267-292.
S. Benzoni-Gavage,
F. Rousset,
D. S. &
K. Zumbrun,
Generic types and transitions in hyperbolic
initial-boundary value problems. Proceedings (A)
of the Royal Soc. of Edinburgh,
132A (2002) pp 1073-1104.
S. Benzoni-Gavage,
F. Rousset,
D. S. &
K. Zumbrun,
Classes persistantes de problèmes mixtes hyperboliques
(Résumé en
Français du précédent). Colloque Tuniso-Français
d'EDPs.
La Marsa, 17-22 Avril 2001. Eds B. Dehman, G. Lebeau, C. Zuily.
Société Mathématique de Tunisie (2002), pp 155-167.
D. S. Asymptotics of homogeneous oscillations in a
compressible viscous fluid. Bol. Soc. Bras. Mat., 32, No 3
(2002), pp 435-442.
Numéro spécial en l'honneur de
Constantin Dafermos.
M. Hillairet & D. S. Chute stationnaire d'un solide dans un fluide
visqueux
incompressible le long d'un plan incliné. Ann. de l'Inst. Henri
Poincaré, Anal. non linéaire, 20 (2003),
pp 779-803.
D. S. The stability of constant equilibrium states in relaxation
models. Annali dell'Universita' di Ferrara, 48 (2002),
pp 253-274.
D. S. L1-Stability of constants in a model for radiating gases.
Communications in Math Sciences, 1 (2003) pp 199-207.
S. Benzoni-Gavage, J.-F. Coulombel & D. S.
Note on a paper by Robinet, Gressier, Casalis and Moschetta.
Journal of Fluid Mechanics, 469 (2002), pp 401-405.
D. S. Hyperbolicity of the non-linear models of Maxwell's equations.
Archive for Rational Mechanics and Analysis,
172 (2004), pp 309-331.
D. S. A convex hull arising in the multi-dimensional
theory of Born-Infeld electro-magnetic fields. Nonlinear PDEs and Related
Analysis (Evanston, 2003) ; G.-Q. Chen, G. Gasper, J. Jerome eds.
Contemporary Math. 311, (2005) pp 265-270.
D. S. Spectral stability
of periodic solutions of viscous conservation laws: Large
wavelength analysis.
Communications in PDEs, 30 (2005), pp 259--282.
T. Ruggeri & D. S. Stability of constant equilibrium state for
dissipative balance laws system
with a convex entropy. Quarterly of Applied Math., 62 (2004),
pp 163-179.
D. S. Systèmes de lois de conservation hyperbolique-elliptique.
Voir au format
PDF (250 K). With an English abridged version. Article rejeté
le 27 septembre 2004.
A. Morando & D. S. A result of L2-well posedness concerning the
system of linear elasticity in 2D.
Communications in Math. Sc., 3 (2005), pp 317-334.
A. Morando & D. S. On the L2-well posedness of an initial boundary
value problem for the 3D linear elasticity.
Communications in Math. Sc., 3 (2005), pp 575-586.
D. S. Solvability of hyperbolic IBVPs through filtering.
Voir au format
PDF. Methods and Applications of Analysis, 12 (2005),
pp 253-266. Volume spécial dédié à
Joel Smoller.
D. S. Second-order initial-boundary value problems of variational type.
Voir
en ligne. J. of Functional Analysis, 236 (2006), pp 409-446.
D. Amadori & D. S. Asymptotic behavior of solutions to conservation laws with
periodic forcing. J. Hyperbolic Differential Equations, 3
(2006), pp 387-401. Volume spécial dédié à
Tai-Ping Liu.
D. S. Second-order initial-boundary value problems of variational type:
the incompressible case.
Voir au format
PDF (260 K). Rendiconti Circ. Mat. Palermo., Serie II, Suppl.
78 (2006), pp 285-312. Volume spécial dédié à
Guy Boillat.
D. S. Waves in Systems of Conservation Laws: Large vs Small
Scales.
Voir au format
PDF (274 K). Proceedings of Hyperbolic Problems: Theory, Numerics
and Applications, vol. I (Osaka, 2004). Yokohama Publishers (2006), pp
45-56.
C. Lattanzio,
C. Mascia & D. S. Shock waves for radiative
hyperbolic-elliptic systems.
Voir au format
PDF. Indiana Univ. Math. J., 56 (2007), pp 2601-2640.
S. Benzoni-Gavage,
D. S. &
K. Zumbrun, Transition to instability of planar viscous shock fronts:
the refined stability condition.
Voir au format
PDF. J. of Analysis and its applications (ZAA), 27 (2008), pp 381-406.
D. S. Non-linear electromagnetism and special relativity.
Voir au format
PDF (235 K). Discrete Cont. Dynam. Syst., 23 (2009), pp 435-454.
D. S. Multi-dimensional shock interaction for a Chaplygin gas.
Voir au format
PDF (350 K). Arch. Rational Mech. Anal., 191 (2009), pp 539-577.
Nota: this paper contains a proof of existence and uniqueness of a solution of
some degenerate elliptic BVP. Lihe Wang (personal communication, 2011)
observed that such solutions describe complete minimal graphs in the 3D-hyperbolic space. This existence result was originally claimed by M. Anderson (Inventiones Math. 1982, Theorem 10). However, the author did not pay attention to the non-uniform ellipticity, and contents himself to provide upper/lower bounds. Therefore his arguments do not form a proof.
In a follow-up, Fang Hua Lin (Inventiones Math. 1989) considered the boundary regularity. He recalled Anderson's result (Theorem 2.1) and gave again a proof, which suffers the same weakness.
D. S. The structure of dissipative viscous system of
conservation laws. Physica D293 (2010), pp 1381-1386.
D. S. Local existence for viscous system of conservation laws:
Hs-data with s > 1 + d/2. Nonlinear PDEs and Hyperbolic Wave Phenomena.
H. Holden, K. Karlsen eds. Contemporary Math. 526 (2010), pp 339-358.
D. S. Weyl and Lidskii inequalities for general hyperbolic
polynomials. Chinese Annals of Maths., 30B (2009),
DOI
10.1007/s11401-009-0169-3 (207 K).
D. S. Viscous system of conservation laws: Singular limits. IMA volume 153:
Nonlinear Conservation Laws and Appl. A. Bressan, G.-Q. Chen, M. Lewicka,
D. Wang eds. Springer-Verlag (2010), pp 433-445. Voir au format
PDF (191 K).
T. Gallay, D. S. The numerical measure of a complex matrix. Comm.
Pure and Appl. Math., 65 (2012), pp 287-336.
Voir au format
PDF (602 K).
D. S. Irrotational flows for Chaplygin gas. Conical waves. Proceedings of
HYP2010 (Beijing, 2010) Li Da-Qian and Song Jiang eds. CAM 17, Higher Education Press (Beijing), pp 102-119. Voir au format
PDF (825 K).
D. S. Three-dimensional interaction of shocks in irrotational flows. Confluentes Mathematici, 3 (2011), pp 543-576. Voir au format PDF (626 K).
D. S. Five open problems in compressible mathematical fluid dynamics. Methods and Applications in Analysis, 20 (2013) pp 197-210. Voir au format PDF (178 K).
D. S., H. Freistühler, The hyperbolic/elliptic transition in the multi-dimensional Riemann Problem. Indiana Univ. Math. J. 62 (2013), no 2, pp 465-485. Voir au format PDF (333 K).
D. S., A. Vasseur, L2-type contraction for systems of conservation laws. Journal de l'École polytechnique; Mathématiques 1 (2014) pp 1-28. Voir au format PDF.
D. S. About the Young measures associated with Y. Brenier's ABI model. Journal of Differential Equations, 256 (2014), no 11, pp 3709-3720. Voir au format PDF (178 K).
D. S. Long-time stability in systems of conservation laws, using relative entropy/energy. Archive for Rational Mechanics and Analysis 219 (2015), no 2, pp 679-699. Voir au format PDF (178 K).
D. S. The reverse Hlawka inequality in a Minkowski space. Voir au format PDF. Comptes Rendus Math. 353 (2015), no 7, pp 629-633.
D. S., A. Vasseur, About the relative entropy method for hyperbolic systems of conservation laws. Contemporary Mathematics. Special volume for the Conference on Mathematics and its Applications 2014, Kuwait University. 658 (2016). Voir au format PDF.
D. S. Expansion of a compressible gas in vacuum. Voir au format PDF. Bulletin of the Institute of Mathematics, Academia Sinica, Taiwan. 10 (2015), pp 695-716. Online.
D. S. Gradient estimates in terms of a Hilbert-like distance, for minimal surfaces and Chaplygin gas. Voir au format PDF. Communications in PDE 41 (2016), pp 774-784.
D. S., A. Vasseur, The relative entropy method for the stability of intermediate shock waves ; the rich case. Version révisée. Discrete and continuous Dynamical Systems, 36 volume dédié à P. D. Lax (2016), pp 4569-4577.
D. S. Non-commutative standard polynomials applied to matrices. Voir l'article dans Linear Algebra and its Applications 490 (2016), pp 202-223.
D. S. The role of the Hilbert metric in a class of singular elliptic boundary value problems in convex domains. Confluentes Mathematici 9 (2017), pp 105-117.
D. S. The helicity and other conservation laws in perfect fluid motion. En mémoire de J.-J. Moreau. Comptes Rendus Mécanique, 346 (2018), pp 175-183.
D. S. Divergence-free positive symmetric tensors and fluid dynamics. Annales de l'IHP, analyse non linéaire, 35 (2018), pp 1209-1234. Voir PDF. Read also the improvement of Theorem 2.3. Read also a comment on the positivy assumption in Theorem 2.3.
D. S. Periodic homogenization in terms of differential forms. Revue Roumaine de Maths Pures et Appl., 63 (2018), pp 527-546. Voir au format PDF.
D. S. Compensated integrability. Applications to the Vlasov-Poisson equation and other models of mathematical physics. Journal de Mathématiques Pures et Appliquées, 127 (2019), pp 67-88. Voir au format PDF.
D. S., L. Silvestre, Multi-dimensional scalar conservation laws with unbounded initial data: well-posedness and dispersive estimates. Arch. Rat. Mech. Anal., 234 (2019), pp 1391-1411. Preprint arXiv1808.07467.
D. S. Divergence et déterminant des tenseurs symétriques positifs. Séminaire Laurent Schwartz, École Polytechnique (2018--19), Exposé numéro V. Voir au format PDF.
D. S. Hard spheres dynamics: weak vs strong collisions. Arch. Rat. Mech. Anal., 240 (2021), pp 243-264. Voir au format PDF.
L. De Rosa, D. S., R. Tione. On the upper semicontinuity of a quasiconcave functional. J. Functional Analysis, 279 (2020).
D. S. Source-solutions for the multi-dimensional Burgers equation. Arch. Rat. Mech. Anal., 239 (2019), pp 95-116. Preprint, voir au format PDF.
D. S. L2-type Lyapunov functions for hyperbolic scalar conservation laws. Communications in PDEs (2021), voir au format PDF.
D. S. Projective Properties of Divergence-Free Symmetric Tensors, and New Dispersive Estimates in Gas Dynamics. Milan J. Maths (2021), voir au format PDF.
D. S. Asymptotic stability of scalar multi-D inviscid shock waves. Soumis (2021), voir au format PDF.
D. S. L2-type Symmetric Divergence-free tensors in the Calculus of Variations. Prépublication (2021), voir au format PDF.
Notes de cours : Vulgarisation :
Recension :
J. Levelt-Sengers. How fluids unmix.
Discoveries by the school of van der Waals and Kamerlingh Onnes.
Koninklijke Nederlandse Akademie van Wetenschappen, Amsterdam, 2002.
Pour
Math. Reviews (43 K).
Traduction :
Donald E. Knuth. 3:16 Bible en lumière. Bayard, 2017.
ISBN 978-2-2274-9168-7
