Cauchy problem for effectively hyperbolic operators with triple characteristics of variable multiplicity
| hal.structure.identifier | Matemates | |
| dc.contributor.author | BERNARDI, Enrico | |
| dc.contributor.author | BOVE, Antonio | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PETKOV, Vesselin | |
| dc.date.accessioned | 2024-04-04T02:19:20Z | |
| dc.date.available | 2024-04-04T02:19:20Z | |
| dc.date.created | 2013-12-11 | |
| dc.date.issued | 2015-09 | |
| dc.identifier.issn | 0219-8916 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189393 | |
| dc.description.abstractEn | We study a class of third order hyperbolic operators $P$ in $G = \{(t, x):0 \leq t \leq T, x \in U \Subset \R^{n}\}$ with triple characteristics at $\rho = (0, x_0, \xi), \xi \in \R^n \setminus \{0\}$. We consider the case when the fundamental matrix of the principal symbol of $P$ at $\rho$ has a couple of non-vanishing real eigenvalues. Such operators are called {\it effectively hyperbolic}. V. Ivrii introduced the conjecture that every effectively hyperbolic operator is {\it strongly hyperbolic}, that is the Cauchy problem for $P + Q$ is locally well posed for any lower order terms $Q$. This conjecture has been solved for operators having at most double characteristics and for operators with triple characteristics in the case when the principal symbol admits a factorization. A strongly hyperbolic operator in $G$ could have triple characteristics in $G$ only for $t = 0$ or for $t = T$. We prove that the operators in our class are strongly hyperbolic if $T$ is small enough. Our proof is based on energy estimates with a loss of regularity. | |
| dc.description.sponsorship | Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution - ANR-11-BS01-0019 | |
| dc.language.iso | en | |
| dc.publisher | World Scientific Publishing | |
| dc.subject.en | Cauchy Problem | |
| dc.subject.en | Effectively Hyperbolic Operators | |
| dc.subject.en | Triple Characteristics | |
| dc.subject.en | Energy estimates | |
| dc.title.en | Cauchy problem for effectively hyperbolic operators with triple characteristics of variable multiplicity | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1303.0950 | |
| bordeaux.journal | Journal of Hyperbolic Differential Equations | |
| bordeaux.page | 535-579. | |
| bordeaux.volume | 12 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00953693 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00953693v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Hyperbolic%20Differential%20Equations&rft.date=2015-09&rft.volume=12&rft.issue=3&rft.spage=535-579.&rft.epage=535-579.&rft.eissn=0219-8916&rft.issn=0219-8916&rft.au=BERNARDI,%20Enrico&BOVE,%20Antonio&PETKOV,%20Vesselin&rft.genre=article |
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