Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 2, p. 327-358

We prove that the Cauchy problem for a class of hyperbolic equations with non-Lipschitz coefficients is well-posed in 𝒞 ∞ and in Gevrey spaces. Some counter examples are given showing the sharpness of these results.

Classification:  35L15,  35L10,  35A05
@article{ASNSP_2002_5_1_2_327_0,
     author = {Colombini, Ferruccio and Del Santo, Daniele and Kinoshita, Tamotu},
     title = {Well-posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {2},
     year = {2002},
     pages = {327-358},
     zbl = {1098.35094},
     mrnumber = {1991143},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_2_327_0}
}
Colombini, Ferruccio; del Santo, Daniele; 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, Serie 5, Volume 1 (2002) no. 2, pp. 327-358. http://www.numdam.org/item/ASNSP_2002_5_1_2_327_0/

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