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Busuioc, Valentina; Gallay, Thierry; Joly, Romain

In memoriam: Geneviève Raugel. (English) Zbl 1498.01021

J. Dyn. Differ. Equations 34, No. 4, 2585-2592 (2022).

MSC:

01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Raugel, Geneviève
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[1] Raugel, G., Résolution numérique par une méthode d’éléments finis du problème de Dirichlet pour le laplacien dans un polygone. C. R. Acad. Sci., Paris, Sér. A, 286, 791-794 (1978) · Zbl 0377.65058
[2] Bernardi, C.; Raugel, G., Analysis of some finite elements for the Stokes problem, Math. Comput., 44, 71-79 (1985) · Zbl 0563.65075
[3] Geymonat, G., Raugel, G.: Finite dimensional approximation of some bifurcation problems in presence of symmetries. Numerical methods for bifurcation problems, Proc. Conf., Dortmund/Ger. 1983, ISNM 70, 369-384 (1984)., 1984 · Zbl 0599.73039
[4] Crouzeix, M.; Geymonat, G.; Raugel, G., Some remarks about the Morse lemma in infinite dimension, SIAM J. Math. Anal., 19, 2, 358-371 (1988) · Zbl 0652.58017
[5] Hale, JK; Lin, X-B; Raugel, G., Upper semicontinuity of attractors for approximations of semigroups and partial differential equations, Math. Comput., 50, 181, 89-123 (1988) · Zbl 0666.35013
[6] Hale, J.K., Raugel, G.: Partial differential equations on thin domains. In Slow motion manifolds for a class of singular perturbation problems: The linearized equations, pp. 63-97. (1992) · Zbl 0785.35050
[7] Hale, JK; Raugel, G., A damped hyperbolic equation on thin domains, Trans. Am. Math. Soc., 329, 1, 185-219 (1992) · Zbl 0761.35052
[8] Hale, JK; Raugel, G., Reaction-diffusion equation on thin domains, J. Math. Pures Appl. (9), 71, 1, 33-95 (1992) · Zbl 0840.35044
[9] Hale, J.K., Raugel, G.: Attractors and convergence of PDE on thin L-shaped domains. In Progress in partial differential equations: the Metz surveys 2. Proceedings of the conferences given at the University of Metz (France) during the 1992 “Metz Days”, pp. 149-171. Harlow: Longman Scientific & Technical, (1993) · Zbl 0806.35076
[10] Hale, JK; Raugel, G., A reaction-diffusion equation on a thin \(L\)-shaped domain, Proc. R. Soc. Edinb. Sect. A, Math., 125, 2, 283-327 (1995) · Zbl 0828.35055
[11] Raugel, G.: Dynamics of partial differential equations on thin domains. In Dynamical systems. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Montecatini Terme, Italy, June 13-22, 1994, pp. 208-315. Berlin: Springer-Verlag (1995) · Zbl 0851.58038
[12] Hale, JK; Raugel, G., Regularity, determining modes and Galerkin methods, J. Math. Pures Appl. (9), 82, 9, 1075-1136 (2003) · Zbl 1043.35048
[13] Hale, JK; Raugel, G., A modified Poincaré method for the persistence of periodic orbits and applications, J. Dyn. Differ. Equ., 22, 1, 3-68 (2010) · Zbl 1189.35018
[14] Hale, J.K., Raugel, G.: Persistence of periodic orbits for perturbed dissipative dynamical systems. In: Infinite dimensional dynamical systems. Collected papers of the international conference, Toronto, Canada, September 24-28, 2008, pp. 1-55. New York, NY: Springer; Toronto: Fields Institute for Research in Mathematical Sciences (2012) · Zbl 1263.35016
[15] Raugel, G.; Sell, GR, Équations de Navier-Stokes dans des domaines minces en dimension trois: Régularité globale, C. R. Acad. Sci. Paris, Sér. I, 309, 6, 299-303 (1989) · Zbl 0715.35063
[16] Raugel, G.; Sell, GR, Navier-Stokes equations on thin 3D domains. I: Global attractors and global regularity of solutions, J. Am. Math. Soc., 6, 3, 503-568 (1993) · Zbl 0787.34039
[17] Raugel, G., Sell, G.R.: Navier-Stokes equations on thin 3D domains. II: Global regularity of spatially periodic solutions. In: Nonlinear partial differential equations and their applications. Collège de France Seminar, volume XI. Lectures presented at the weekly seminar on applied mathematics, Paris, France, 1989-1991, pp. 205-247. Harlow: Longman Scientific & Technical; New York: John Wiley & Sons, Inc. (1994) · Zbl 0804.35106
[18] Raugel, G., Sell, G.R.: Navier-Stokes equations in thin 3D domains. III: Existence of a global attractor. In: Turbulence in fluid flows. A dynamical systems approach. Proceedings of a workshop which was an integral part of the 1989-90 IMA program on “Dynamical systems and their applications”, Minneapolis, MN (USA), pp. 137-163. New York: Springer-Verlag (1993) · Zbl 0804.76024
[19] Marsden, J.E., Ratiu, T., Raugel, G.: Symplectic connections and the linearisation of Hamiltonian systems. Proc. R. Soc. Edinb. Sect. A Math. 117(3-4), 329-380 (1991) · Zbl 0795.58018
[20] Marsden, J.E., Ratiu, T.S., Raugel, G.: The Euler equations on thin domains. In: International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 2, pp. 1198-1203. Singapore: World Scientific, (2000) · Zbl 0993.76008
[21] Iftimie, D.; Raugel, G., Some results on the Navier-Stokes equations in thin 3D domains, J. Differ. Equ., 169, 2, 281-331 (2001) · Zbl 0972.35085
[22] Iftimie, D.; Raugel, G.; Sell, GR, Navier-Stokes equations in thin 3D domains with Navier boundary conditions, Indiana Univ. Math. J., 56, 3, 1083-1156 (2007) · Zbl 1129.35056
[23] Paicu, M.; Raugel, G., Une perturbation hyperbolique des équations de Navier-Stokes, ESAIM Proc., 21, 65-87 (2007) · Zbl 1221.35284
[24] Paicu, M., Raugel, G.: Anisotropic Navier-Stokes equations in a bounded cylindrical domain. In: Partial differential equations and fluid mechanics. Result of a workshop, Warwick, UK, May 21-23, 2007, pp. 146-184. Cambridge: Cambridge University Press (2009) · Zbl 1185.35172
[25] Paicu, M.; Raugel, G.; Rekalo, A., Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations, J. Differ. Equ., 252, 6, 3695-3751 (2012) · Zbl 1235.35225
[26] Paicu, M., Raugel, G.: Dynamics of second grade fluids: the Lagrangian approach. In: Recent trends in dynamical systems. Proceedings of the international conference, Munich, Germany, January 11-13, 2012, in honor of Jürgen Scheurle on the occasion of his 60th birthday, pp. 517-553. Basel: Springer (2013) · Zbl 1318.35086
[27] Ngo, V-S; Raugel, G., Approximate controllability of second-grade fluids, J. Dyn. Control Syst., 27, 3, 531-556 (2021) · Zbl 1475.35285
[28] Kirchgässner, K., Raugel, G.: Stability of fronts for a KPP-system – the noncritical case. In: Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability, pp. 147-208, 263-277. Harlow: Longman, (1996) · Zbl 0866.35005
[29] Raugel, G.; Kirchgässner, K., Stability of fronts for a KPP-system, II: the critical case, J. Differ. Equ., 146, 2, 399-456 (1998) · Zbl 0913.35056
[30] Gallay, T.; Raugel, G., Stability of travelling waves for a damped hyperbolic equation, Z. Angew. Math. Phys., 48, 3, 451-479 (1997) · Zbl 0877.35021
[31] Gallay, T.; Raugel, G., Scaling variables and asymptotic expansions in damped wave equations, J. Differ. Equ., 150, 1, 42-97 (1998) · Zbl 0913.35086
[32] Gallay, T., Raugel, G.: Stability of propagating fronts in damped hyperbolic equations. In Partial differential equations: theory and numerical solution. Proceedings of the ICM’98 satellite conference, Prague, Czech Republic, August 10-16, 1998, pp. 130-146. Boca Raton, FL: Chapman & Hall/CRC, (2000) · Zbl 0931.35103
[33] Gallay, T.; Raugel, G., Scaling variables and stability of hyperbolic fronts, SIAM J. Math. Anal., 32, 1, 1-29 (2000) · Zbl 0963.35128
[34] Gallay, Thierry, J., Romain, R.G.: Asymptotic self-similarity in diffusion equations with nonconstant radial limits at infinity. To be published in J. Dyn. Differ. Equ. (2021)
[35] Brunovský, P.; Raugel, G., Genericity of the Morse-Smale property for damped wave equations, J. Dyn. Differ. Equ., 15, 2-3, 571-658 (2003) · Zbl 1053.35099
[36] Joly, R.; Raugel, G., Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle, Trans. Am. Math. Soc., 362, 10, 5189-5211 (2010) · Zbl 1205.35151
[37] Joly, R.; Raugel, G., Generic Morse-Smale property for the parabolic equation on the circle, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 27, 6, 1397-1440 (2010) · Zbl 1213.35046
[38] Brunovský, P., Joly, R., Raugel, G.: Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations. To be published in J. Dyn. Differ. Equ. (2021)
[39] Burq, N.; Raugel, G.; Schlag, W., Dynamique en temps grand des solutions de l’équation de Klein-Gordon amortie, Ann. Sci. Éc. Norm. Supér. (4), 50, 6, 1447-1498 (2017) · Zbl 1392.35041
[40] Bernardi, C.; Godlewski, E.; Raugel, G., A mixed method for the time-dependent Navier-Stokes problem, IMA J. Numer. Anal., 7, 165-189 (1987) · Zbl 0652.76018
[41] Bernardi, C.; Raugel, G., Méthodes d’éléments finis mixtes pour les équations de Stokes et de Navier-Stokes dans un polygone non convexe, Calcolo, 18, 255-291 (1981) · Zbl 0475.76035
[42] Bernardi, C.; Raugel, G., Approximation numérique de certaines équations paraboliques non linéaires, RAIRO Anal. Numér., 18, 237-285 (1984) · Zbl 0548.65071
[43] Bernardi, C.; Raugel, G., A conforming finite element method for the time-dependent Navier-Stokes equations, SIAM J. Numer. Anal., 22, 455-473 (1985) · Zbl 0578.65122
[44] Bortolan, M.C., de Carvalho, A.N., Langa, J.A., Raugel, G.: Nonautonomous perturbations of Morse-Smale semigroups: stability of the phase diagram. To be published in J. Dyn. Differ. Equ. (2021)
[45] Chueshov, ID; Raugel, G.; Rekalo, AM, Interface boundary value problem for the Navier-Stokes equations in thin two-layer domains, J. Differ. Equ., 208, 2, 449-493 (2005) · Zbl 1078.35084
[46] Crouzeix, M.; Raugel, G., Invariance under the dihedral group and application to bifurcation problems, Nonlinear Anal. Theory Methods Appl., 12, 1, 75-99 (1988) · Zbl 0662.58030
[47] Hale, JK; Raugel, G., Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Differ. Equ., 73, 2, 197-214 (1988) · Zbl 0666.35012
[48] Hale, JK; Raugel, G., Lower semicontinuity of attractors of gradient systems and applications, Ann. Mat. Pura Appl., 4, 154, 281-326 (1989) · Zbl 0712.47053
[49] Hale, JK; Raugel, G., Lower semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Dyn. Differ. Equ., 2, 1, 19-67 (1990) · Zbl 0752.35034
[50] Hale, JK; Raugel, G., Convergence in gradient-like systems with applications to PDE, Z. Angew. Math. Phys., 43, 1, 63-124 (1992) · Zbl 0751.58033
[51] Hale, J.K., Raugel, G.: Attractors for dissipative evolutionary equations. In: International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Barcelona, Spain, August 26-31, 1991, pp. 3-22. Singapore: World Scientific, (1993) · Zbl 0938.34536
[52] Hale, J.K., Raugel, G.: Limits of semigroups depending on parameters. Resen. Inst. Mat. Estat. Univ. São Paulo, 1(1), 1-45 (1993) (figures no. 2-3, 361) · Zbl 0863.58046
[53] Hale, J.K., Raugel, G.: Galerkin methods and regularity. In: Differential equations and dynamical systems. Papers of the conference, Lisbon, Portugal, June 26-30, 2000, pp. 173-188. Providence, RI: American Mathematical Society (AMS), (2002) · Zbl 1010.35018
[54] Joly, R.; Raugel, G., A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations, Conflu. Math., 3, 3, 471-493 (2011) · Zbl 1241.35001
[55] Marsden, JE; Ratiu, TS; Raugel, G., Équations d’Euler dans une coque sphérique mince, C. R. Acad. Sci., Paris, Sér. I, 321, 9, 1201-1206 (1995) · Zbl 0837.76077
[56] Mercier, B.; Raugel, G., Résolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en \(r,z\) et séries de Fourier en \(\theta \). RAIRO, Anal. Numér., 16, 405-461 (1982) · Zbl 0531.65054
[57] Rappaz, J., Raugel, G.: Approximation of double bifurcation points for nonlinear eigenvalue problems. The mathematics of finite elements and applications IV, MAFELAP 1981, In: Proc. Conf., Uxbridge/Middlesex 1981, 453-461 (1982)., 1982 · Zbl 0571.65048
[58] Raugel, G., Finite dimensional approximation of bifurcation problems in presence of symmetries, Numer. Math., 48, 137-198 (1986) · Zbl 0562.65073
[59] Raugel, G., Stabilité d’une équation parabolique de Morse-Smale perturbée de manière singulière en une équation hyperbolique, C. R. Acad. Sci., Paris, Sér. I, 310, 3, 85-88 (1990) · Zbl 0704.35004
[60] Raugel, G., Une équation des ondes avec amortissement non linéaire dans le cas critique en dimension trois, C. R. Acad. Sci., Paris, Sér. I, 314, 3, 177-182 (1992) · Zbl 0761.35065
[61] Raugel, G.: Singularly perturbed hyperbolic equations revisited. In: International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1, pp. 647-652. Singapore: World Scientific (2000) · Zbl 0969.35089
[62] Raugel, G.: Global attractors in partial differential equations. In: Handbook of dynamical systems. Volume 2, pp. 885-982. Amsterdam: Elsevier (2002) · Zbl 1005.35001
[63] Raugel, G.; Hale, JK, Continuity of attractors. RAIRO, Modélisation Math, Anal. Numér., 23, 3, 519-533 (1989) · Zbl 0687.58021
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