# On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in $t$ and degenerate in $t=T$

Rendiconti del Seminario Matematico della Università di Padova (1998)

- Volume: 100, page 81-96
- ISSN: 0041-8994

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topKinoshita, Tamotu. "On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in $t$ and degenerate in $t = T$." Rendiconti del Seminario Matematico della Università di Padova 100 (1998): 81-96. <http://eudml.org/doc/108465>.

@article{Kinoshita1998,

author = {Kinoshita, Tamotu},

journal = {Rendiconti del Seminario Matematico della Università di Padova},

keywords = {order of degeneration; Levi conditions},

language = {eng},

pages = {81-96},

publisher = {Seminario Matematico of the University of Padua},

title = {On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in $t$ and degenerate in $t = T$},

url = {http://eudml.org/doc/108465},

volume = {100},

year = {1998},

}

TY - JOUR

AU - Kinoshita, Tamotu

TI - On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in $t$ and degenerate in $t = T$

JO - Rendiconti del Seminario Matematico della Università di Padova

PY - 1998

PB - Seminario Matematico of the University of Padua

VL - 100

SP - 81

EP - 96

LA - eng

KW - order of degeneration; Levi conditions

UR - http://eudml.org/doc/108465

ER -

## References

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- [2] F. Colombini - E. De Giorgi - S. Spagnolo, Sur les equations hyperboliques avec des coefficients qui ne d6pendent que du temps, Ann. Scuola Norm. Sup. Pisa, 6 (1979), pp. 511-559. Zbl0417.35049MR553796
- [3] F. Colombini - E. Jannelli - S. Spagnolo, Wellposedness in the Gevrey classes of the Cauchy problem for a non strictly hyperbolic equation with coefficients depending on time, Ann. Scuola Norm. Sup. Pisa, 10 (1983), pp. 291-312. Zbl0543.35056MR728438
- [4] P. D'Ancona, Gevrey well posedness of an abstract Cauchy problem of weakly hyperbolic type, Publ. RIMS Kyoto Univ., 24 (1988), pp. 433-449. Zbl0706.35077MR966182
- [5] P. D'Ancona, Local existence for semilinear weakly hyperbolic equations with time dependent coefficients, Nonlinear Analysis. Theory, Methods and Applications, Vol 21, No. 9 (1993), pp. 685-696. Zbl0830.35089MR1246287
- [6] V. Ya.IVRII, Cauchy problem conditions for hyperbolic operators with characteristics of variable multiplicity for Gevrey classes, Siberian. Math., 17 (1976), pp. 921-931. Zbl0404.35068
- [7] K. Kajitani, The well posed Cauchy problem for hyperbolic operators, Exposé au Séminaire de Vaillant du 8 février (1989).
- [8] T. Kinoshita, On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic systems with Hölder continuous coefficients in t, preprint. Zbl0933.35119
- [9] M. Reissig - K. Yagdjian, Levi conditions and global Gevrey regularity for the solutions of quasilinear weakly hyperbolic equations, Mathematische Nachrichten, 178 (1996), pp. 285-307. Zbl0848.35078MR1380714
- [10] T. Nishitani, Sur les équations hyperboliues à coefficients hölderiens en t et de classes de Gevrey en x, Bull. Sci. Math., 107 (1983), pp. 739-773. Zbl0552.35051MR704720
- [11] H. Odai, On the Cauchy problem for a hyperbolic equation of second order, Doctoral thesis (1994). Zbl0802.11043

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