COLOMBINI, Ferruccio; SANTO, Daniele; FANELLI, Francesco; MÉTIVIER, Guy

doi:10.1512/iumj.2020.69.7963

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Licencia de uso del documento

COLOMBINI, Ferruccio
Dipartimento di Matematica

SANTO, Daniele
Dipartimento di Matematica e Geoscienze [Trieste]

FANELLI, Francesco
Équations aux dérivées partielles, analyse [EDPA]

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Article de revue

Este ítem está publicado en

Indiana University Mathematics Journal. 2020, vol. 69, n° 3

Indiana University Mathematics Journal

Resumen en inglés

The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space problem we establish energy estimates with finite loss of derivatives, which is linearly increasing in time. This implies well-posedness in H ∞ , if the coefficients enjoy enough smoothness in x. From this result, by standard arguments (i.e. extension and convexification) we deduce also local existence and uniqueness. A huge part of the analysis is devoted to give an appropriate sense to the Cauchy problem, which is not evident a priori in our setting, due to the very low regularity of coefficients and solutions. 2010 Mathematics Subject Classification: 35L45 (primary); 35B45, 35B65 (secondary).< Leer menos

Palabras clave en inglés

hyperbolic systems

microlocal symmetrizability

log-Lipschitz regularity

loss of derivatives

global and local Cauchy problem

well-posedness

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193950

DOI

http://dx.doi.org/10.1512/iumj.2020.69.7963

Proyecto ANR

Community of mathematics and fundamental computer science in Lyon - ANR-10-LABX-0070
Bords, oscillations et couches limites dans les systèmes différentiels - ANR-16-CE40-0027

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251