Mersenne banner

Livres, Actes et Séminaires du Centre Mersenne

  • Livres
  • Séminaires
  • Congrès
  • Tout
  • Auteur
  • Titre
  • Bibliographie
  • Plein texte
NOT
Entre et
  • Tout
  • Auteur
  • Titre
  • Date
  • Bibliographie
  • Mots-clés
  • Plein texte
  • Précédent
  • Journées équations aux dérivées partielles
  • Année 2010
  • article no. 4
  • Suivant
Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity
Enrico Bernardi1 ; Antonio Bove2 ; Vesselin Petkov3
1 Dipartimento di Matematica per le Scienze Economiche e Sociali, Università di Bologna, Viale Filopanti 5, 40126 Bologna, Italia
2 Dipartamento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italia
3 Université Bordeaux I, Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France
Journées équations aux dérivées partielles (2010), article no. 4, 13 p.
  • Résumé

We study a class of third order hyperbolic operators P in G=Ω∩{0≤t≤T},Ω⊂ℝ n+1 with triple characteristics on t=0. We consider the case when the fundamental matrix of the principal symbol for t=0 has a couple of non vanishing real eigenvalues and P is strictly hyperbolic for t>0. We prove that P is strongly hyperbolic, that is the Cauchy problem for P+Q is well posed in G for any lower order terms Q.

  • Détail
  • Export
  • Comment citer
DOI : 10.5802/jedp.61
Affiliations des auteurs :
Enrico Bernardi 1 ; Antonio Bove 2 ; Vesselin Petkov 3

1 Dipartimento di Matematica per le Scienze Economiche e Sociali, Università di Bologna, Viale Filopanti 5, 40126 Bologna, Italia
2 Dipartamento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italia
3 Université Bordeaux I, Institut de Mathématiques de Bordeaux, 351, Cours de la Libération, 33405 Talence, France
  • BibTeX
  • RIS
  • EndNote
@incollection{JEDP_2010____A4_0,
     author = {Enrico Bernardi and Antonio Bove and Vesselin Petkov},
     title = {Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {4},
     pages = {1--13},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2010},
     doi = {10.5802/jedp.61},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.61/}
}
TY  - JOUR
AU  - Enrico Bernardi
AU  - Antonio Bove
AU  - Vesselin Petkov
TI  - Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity
JO  - Journées équations aux dérivées partielles
PY  - 2010
SP  - 1
EP  - 13
PB  - Groupement de recherche 2434 du CNRS
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.61/
DO  - 10.5802/jedp.61
LA  - en
ID  - JEDP_2010____A4_0
ER  - 
%0 Journal Article
%A Enrico Bernardi
%A Antonio Bove
%A Vesselin Petkov
%T Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity
%J Journées équations aux dérivées partielles
%D 2010
%P 1-13
%I Groupement de recherche 2434 du CNRS
%U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.61/
%R 10.5802/jedp.61
%G en
%F JEDP_2010____A4_0
Enrico Bernardi; Antonio Bove; Vesselin Petkov. Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity. Journées équations aux dérivées partielles (2010), article  no. 4, 13 p. doi : 10.5802/jedp.61. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.61/
  • Bibliographie
  • Cité par

[1] E. Bernardi, A. Bove, V. Petkov, The Cauchy problem for effectively hyperbolic operators with triple characteristics, in preparation.

[2] J. M. Bony, Sur l’inégalité de Fefferman-Phong, Séminaire EDP, Ecole Polytechnique, 1998-1999. | Numdam | MR

[3] J. Chazarain, Opérateurs hyperboliques à caractéristiques de multiplicité constante, Ann. Institut Fourier (Grenoble), 24 (1974), 173-202. | Numdam | MR | Zbl

[4] H. Flashka and G. Strang, The correctness of the Cauchy problem, Adv. in Math. 6 (1971), 347-379. | MR | Zbl

[5] L. Hörmander, Cauchy problem for differential operators with double characteristics, J. Analyse Math. 32 (1977), 118-196. | MR | Zbl

[6] L. Hörmander, Analysis of Linear Partial Differential Operators, III, Springer-Verlag, 1985, Berlin. | MR | Zbl

[7] V. Ja. Ivrii and V. M. Petkov, Necessary conditions for the Cauchy problem for non-strictly hyperboilic equations to be well posed, Uspehi Mat. Nauk, 29: 5 (1974), 1-70 (in Russian), English translation: Russian Math. Surveys, 29:5 (1974), 3-70. | MR | Zbl

[8] V. Ivrii, Sufficient conditions for regular and completely regular hyperbolicity, Trudy Moskov Mat. Obsc.,33 (1976), 3-66 (in Russian), English translation: Trans. Moscow Math. Soc. 1 (1978), 165. | MR | Zbl

[9] N. Iwasaki, The Cauchy problem for effectively hyperbolic equations (a standard type), Publ. RIMS Kyoto Univ. 20 (1984), 551-592. | MR

[10] N. Iwasaki, The Cauchy problem for effectively hyperbolic equations (general case), J. Math. Kyoto Univ. 25 (1985), 727-743. | MR | Zbl

[11] R. Melrose, The Cauchy problem for effectively hyperbolic operators, Hokkaido Math. J. 12 (1983), 371-391. | MR | Zbl

[12] T. Nishitani, Local energy integrals for effectively hyperbolic operators, I, II, J. Math. Kyoto Univ. 24 (1984), 623-658 and 659-666. | MR | Zbl

[13] T. Nishitani, The effectively Cauchy problem in The Hyperbolic Cauchy Problem, Lecture Notes in Mathematics, 1505, Springer-Verlag, 1991, pp. 71-167. | MR

[14] O. A. Oleinik, On the Cauchy problem for weakly hyperbolic equations, Comm. Pure Appl. Math. 23 (1970), 569-586. | MR

[15] M. R. Spiegel, J. Liu, Mathematical handbook of formulas and tables, McGraw-Hill, Second Edition, 1999.

Cité par Sources :

Diffusé par : Publié par : Développé par :
  • Nous suivre