Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

Bernardi, Enrico; Bove, Antonio; Petkov, Vesselin

doi:10.5802/jedp.61

Bernardi, Enrico ¹ ; Bove, Antonio ² ; Petkov, Vesselin 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

Journées équations aux dérivées partielles (2010), article no. 4, 13 p.

Résumé

We study a class of third order hyperbolic operators $P$ in $G = Ω \cap {0 \leq t \leq T}, Ω \subset ℝ^{n + 1}$ 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 $Q$ .

DOI : 10.5802/jedp.61

Affiliations des auteurs :

Bernardi, Enrico ¹ ; Bove, Antonio ² ; Petkov, Vesselin ³

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Bernardi, Enrico; Bove, Antonio; Petkov, Vesselin. 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. http://www.numdam.org/articles/10.5802/jedp.61/

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