bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Gramchev, Todor and Rodino, Luigi:
Gevrey solvability for semilinear partial differential equations with multiple characteristics
Bollettino dell'Unione Matematica Italiana Serie 8 2-B (1999), fasc. n.1, p. 65-120, Unione Matematica Italiana (English)
pdf (473 Kb), djvu (697 Kb). | MR1794545 | Zbl 0924.35030

Sunto

Vengono considerate equazioni alle derivate parziali semilineari con caratteristiche multiple. Si studia in particolare la loro risolubilità locale e la buona positura del problema di Cauchy nell'ambito delle classi di Gevrey.
Referenze Bibliografiche
[1] S. ALINHAC - P. GÉRARD , Opérateurs pseudo-différentiels et théorème de Nash-Moser, Inter Edition, Editions du CNRS, Meudon, Paris (1991). | MR 1172111 | Zbl 0791.47044
[2] J.-M. BONY , Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sc. École Norm. Sup., 14 (1981), 161-205. | fulltext mini-dml | MR 631751 | Zbl 0495.35024
[3] F. CARDOSO , A necessary condition of Gevrey solvability for differential operators with double characteristics, Comm. Partial Diff. Eqs., 14 (1989), 981-1009. | MR 1017059 | Zbl 0719.35001
[4] W. CRAIG , Nonstrictly hyperbolic nonlinear systems, Math. Ann., 277 (1987), 213-232. | MR 886420 | Zbl 0614.35060
[5] L. CATTABRIGA - L. RODINO - L. ZANGHIRATI , Analytic-Gevrey hypoellipticity for a class of pseudodifferential operators with multiple characteristics, Comm. Partial Diff. Eqs., 15 (1989), 81-96. | MR 1032624 | Zbl 0704.35035
[6] HUA CHEN - L. RODINO , Micro-elliptic Gevrey regularity for nonlinear partial differential equations, Boll. Un. Mat. Ital., 10-B (1996), 199-232. | MR 1385060 | Zbl 0860.35153
[7] M. CICOGNANI - L. ZANGHIRATI , On a class of unsolvable operators, Ann. Scuola Norm. Sup. Pisa, 20 (1993), 357-369. | fulltext mini-dml | MR 1256073 | Zbl 0816.47051
[8] M. CICOGNANI - L. ZANGHIRATI , Analytic regularity for solutions to semi-linear weakly hyperbolic equations, Rend. Sem. Mat. Univ. Politec. Torino, 51 (1993), 387-396. | MR 1289896 | Zbl 0816.35091
[9] A. CORLI , On local solvability in Gevrey classes of linear partial differential operators with multiple characteristics, Comm. Partial Diff. Eqs., 14 (1988), 1-25. | MR 973268 | Zbl 0668.35002
[10] A. CORLI , On local solvability of linear partial differential operators with multiple characteristics, J. Diff. Eqs., 81 (1989), 275-293. | MR 1016083 | Zbl 0701.35002
[11] A. CORLI - L. RODINO , Gevrey solvability for hyperbolic operators with costant multiplicity, in Recent Developments in Hyperbolic Equations, Pitman Res. Notes in Math., 183, 290-304, Longman, Harlow (1988). | MR 984375 | Zbl 0739.35002
[12] P. D'ANCONA - S. SPAGNOLO , On the life span of the analytic solutions to quasilinear weakly hyperbolic equations, Indiana Univ. Math. J., 40, 1 (1991), 71-99. | MR 1101222 | Zbl 0729.35012
[13] P. D'ANCONA - M. REISSIG , New trends in the theory of nonlinear weakly hyperbolic equations of second order, Proc. 2-nd WCNA, Athens, Greece, 10-17 July 1996, Nonl. Anal. TMA, 30, 4 (1997), 2507-2515. | MR 1490366 | Zbl 0890.35076
[14] B. DEHMAN , Resolubilité local pour des équations semi-linéaires complexes, Can. J. Math., 42 (1990), 126-140. | MR 1043515 | Zbl 0718.35027
[15] Y. EGOROV , Linear Differential Equations of Principal Type, Nauka, Moscow (1994); Plenum Press, New York (1985). | Zbl 0669.35001
[16] A. FERRARI - E. TITI , Gevrey regularity for nonlinear analytic parabolic equations, Comm. Partial Diff. Eqs., to appear. | MR 1608488 | Zbl 0907.35061
[17] C. FOIAS - R. TEMAM , Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal., 87 (1989), 359-369. | MR 1026858 | Zbl 0702.35203
[18] G. GARELLO , Local solvability for semilinear equations with multiple characteristics, Ann. Univ. Ferrara, Sez VII, Sc. Mat. Suppl. Vol. 41, 1995 (1997), 199-209. | MR 1471025 | Zbl 0883.35038
[19] R. GOLDMAN , A necessary condition for local solvability of a pseudo-differential equation having multiple characteristics, J. Diff. Eqs., 19 (1975), 176-200. | MR 380171 | Zbl 0305.35085
[20] J. GOODMAN - D. YANG , Local solvability of nonlinear partial differential equations of real principal type, preprint.
[21] D. GOURDIN - M. MECHAB , Problème de Goursat nonlinéaire dans les espaces de Gevrey pour les équations de Kirchhoff généralisées, J. Math. Pures Appl., 75 (1996), 569-593. | MR 1423048 | Zbl 0869.35027
[22] T. GRAMCHEV , Powers of Mizohata type operators in Gevrey classes, Boll. Un. Mat. Ital., (7) 5-B (1991), 135-156. | MR 1110672 | Zbl 0809.47043
[23] T. GRAMCHEV , Nonsolvability for differential operators with multiple complex characteristics, J. Math. Kyoto Univ., 33, 4 (1993), 989-1002. | fulltext mini-dml | MR 1251211 | Zbl 0798.35027
[24] T. GRAMCHEV - P. POPIVANOV , Local solvability of semi-linear partial differential equations, Ann. Univ. Ferrara Sez. VII (N.S.), 25 (1989), 147-154. | MR 1079584 | Zbl 0733.35028
[25] T. GRAMCHEV - M. YOSHINO , Rapidly convergent iteration method for simultaneous normal forms of commuting maps, preprint, 1997. | MR 1709494 | Zbl 0931.65055
[26] V. GRUSHIN , On a class of elliptic pseudodifferential operators degenerate on a submanifold, Mat. Sb., 84 (1971), 163-195 (in russian); Math. USSR Sb., 13 (1971), 155-185. | Zbl 0238.47038
[27] J. HOUNIE , Local solvability of partial differential equations, Rev. Un. Mat. Argentina, 37 (1991), 77-86. | MR 1266670 | Zbl 0813.35003
[28] J. HOUNIE - P. SANTIAGO , On the local solvability of semilinear equations, Comm. Partial Diff. Eqs., 20 (1995), 1777-1789. | MR 1349231 | Zbl 0838.35003
[29] L. HÖRMANDER , The Analysis of Linear Partial Differential Operators, I-IV, Springer-Verlag, Berlin, 1983-85. | Zbl 0521.35001
[30] K. KAJITANI , Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes, Hokkaido Math. J., 12 (1983), 434-460. | MR 725589
[31] K. KAJITANI - S. WAKABAYASHI , Microhyperbolic operators in Gevrey classes, Publ. RIMS Kyoto Univ., 25 (1989), 169-221. | fulltext mini-dml | MR 1003785 | Zbl 0705.35158
[32] J. LERAY - Y. OHYA , Systèmes nonlinéaires hyperboliques nonstricts, Math. Ann., 170 (1967), 167-205. | MR 208136 | Zbl 0146.33701
[33] C. D. LEVERMORE - M. OLIVER , Analyticity of solutions for a generalized Euler equation, J. Diff. Eqs., 133 (1997), 321-339. | MR 1427856 | Zbl 0876.35090
[34] M. MASCARELLO - L. RODINO , Partial Differential Equations with Multiple Characteristics, Akademie Verlag-Wiley, Berlin (1997). | MR 1608649 | Zbl 0888.35001
[35] A. MENIKOFF , Some examples of hypoelliptic partial differential equations, Math. Ann., 221 (1976), 167-181. | MR 481452 | Zbl 0323.35019
[36] Y. MEYER , Remarques sur un théorème de J. M. Bony, Rend. Circ. Mat. Palermo, bf 2, 1 (1981), 1-20. | MR 639462 | Zbl 0473.35021
[37] K. PAYNE , Smooth tame Fréchet algebras and Lie groups of pseudodifferential operators, Comm. Pure Appl. Math., 44 (1991), 309-337. | MR 1090435 | Zbl 0763.47022
[38] T. OKAJI , Gevrey hypoelliptic operators which are not $C^{\infty}$-hypoelliptic, J. Math. Kyoto Univ., 28 (1988), 311-322. | fulltext mini-dml | MR 953179 | Zbl 0684.35032
[39] P. POPIVANOV , A class of differential operators with multiple characteristics which have not solutions, Pliska Stud. Math. Bulg., 3 (1981), 47-60 (Russian). | MR 631966 | Zbl 0497.35018
[40] P. POPIVANOV , On the local solvability of a class of PDE with double characteristics, Trudy Sem. Petrovsk., 1 (1975), 237-278 (Russian); Amer. Math. Soc. Transl., 118, 2 (1982), 51-89. | Zbl 0495.35083
[41] K. PROMISLOW , Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differential equations, Nonl. Anal., TMA, 16 (1991), 959-980. | MR 1106997 | Zbl 0737.35009
[42] J. RAUCH - M. REED , Nonlinear microlocal analysis of semi-linear hyperbolic systems in one space dimension, Duke Math. J., 49 (1982), 397-475. | fulltext mini-dml | MR 659948 | Zbl 0503.35055
[43] M. REISSIG - K. YAGDJIAN , Levi conditions and global Gevrey regularity for the solutions of quasilinear weakly hyperbolic equations, Math. Nachr., 178 (1996), 285-307. | MR 1380714 | Zbl 0848.35078
[44] L. RODINO , Linear Partial Differential Operators in Gevrey Spaces, World Scientific, Singapore, New Jersey, London, Hong Kong (1993). | MR 1249275 | Zbl 0869.35005
[45] M. TAYLOR , Pseudodifferential Operators and Nonlinear PDE, Birkäuser, Boston (1991). | MR 1121019 | Zbl 0746.35062
[46] F. TRÈVES , Introduction to Pseudodifferential Operators and Fourier Integral Operators, vol. I-II, Plenum Press, New York (1980). | Zbl 0453.47027
[47] C. WAGSCHAL , Le problème de Goursat non linéaire, J. Math. Pures Appl., 58 (1979), 309-337. | MR 544256 | Zbl 0427.35021

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali