# Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients

Ferruccio Colombini; Daniele del Santo; Tamotu Kinoshita

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

- Volume: 1, Issue: 2, page 327-358
- ISSN: 0391-173X

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topColombini, Ferruccio, del Santo, Daniele, and Kinoshita, Tamotu. "Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.2 (2002): 327-358. <http://eudml.org/doc/84473>.

@article{Colombini2002,

abstract = {We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in $\{\mathcal \{C\}\}^\infty $ and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.},

author = {Colombini, Ferruccio, del Santo, Daniele, Kinoshita, Tamotu},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

keywords = {strict hyperbolicity},

language = {eng},

number = {2},

pages = {327-358},

publisher = {Scuola normale superiore},

title = {Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients},

url = {http://eudml.org/doc/84473},

volume = {1},

year = {2002},

}

TY - JOUR

AU - Colombini, Ferruccio

AU - del Santo, Daniele

AU - Kinoshita, Tamotu

TI - Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

PY - 2002

PB - Scuola normale superiore

VL - 1

IS - 2

SP - 327

EP - 358

AB - We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in ${\mathcal {C}}^\infty $ and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.

LA - eng

KW - strict hyperbolicity

UR - http://eudml.org/doc/84473

ER -

## References

top- [1] F. Colombini – E. De Giorgi – S. Spagnolo, Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temp, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 6 (1979), 511-559. Zbl0417.35049MR553796
- [2] F. Colombini – D. Del Santo – T. Kinoshita, On the Cauchy problem for hyperbolic operators with non-regular coefficients, to appear in Proceedings of the Conference “À la mémoire de Jean Leray” Karlskrona 2000, M. de Gosson – J. Vaillant (eds.), Kluwer, New York. Zbl1036.35122MR2051477
- [3] F. Colombini – N. Lerner, Hyperbolic operators with non-Lipschitz coefficients, Duke Math. J. 77 (1995), 657-698. Zbl0840.35067MR1324638
- [4] F. Colombini – S. Spagnolo, Some examples of hyperbolic equations without local solvability, Ann. Sci. École Norm. Sup. (4) 22 (1989), 109-125. Zbl0702.35146MR985857
- [5] L. Hörmander, “Linear Partial Differential Operators”, Springer-Verlag, Berlin, 1963. Zbl0108.09301
- [6] E. Jannelli, Regularly hyperbolic systems and Gevrey classes, Ann. Mat. Pura Appl. 140 (1985), 133-145. Zbl0583.35074MR807634
- [7] T. Nishitani, Sur les équations hyperboliques à coefficients höldériens en $t$ et de classe de Gevrey en $x$, Bull. Sci. Math. 107 (1983), 113-138. Zbl0536.35042MR704720

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