Remarks on the Well-Posedness of the Nonlinear Cauchy Problem
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | METIVIER, Guy | |
| dc.date.accessioned | 2024-04-04T03:18:39Z | |
| dc.date.available | 2024-04-04T03:18:39Z | |
| dc.date.issued | 2005 | |
| dc.identifier.issn | 0271-4132 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194430 | |
| dc.description.abstractEn | We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of solutions and we analyze Hadamard's instabilities in Sobolev spaces. We also show that genuinely nonlinear equations raise new interesting problems. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.subject.en | Cauchy Problem | |
| dc.subject.en | well posedness | |
| dc.subject.en | Hadamard's instability | |
| dc.title.en | Remarks on the Well-Posedness of the Nonlinear Cauchy Problem | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | math/0611441 | |
| bordeaux.journal | Contemporary mathematics | |
| bordeaux.page | 337-356 | |
| bordeaux.volume | 368 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00113899 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00113899v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Contemporary%20mathematics&rft.date=2005&rft.volume=368&rft.spage=337-356&rft.epage=337-356&rft.eissn=0271-4132&rft.issn=0271-4132&rft.au=METIVIER,%20Guy&rft.genre=article |
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