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

Tamotu Kinoshita

Rendiconti del Seminario Matematico della Università di Padova (1998)

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

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Kinoshita, 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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  1. [1] M. Cicognani, On the strictly hyperbolic equations which are Hölder continuous with respect to time, preprint. Zbl0967.35087MR1695477
  2. [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. [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. [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. [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. [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. [7] K. Kajitani, The well posed Cauchy problem for hyperbolic operators, Exposé au Séminaire de Vaillant du 8 février (1989). 
  8. [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. [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. [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. [11] H. Odai, On the Cauchy problem for a hyperbolic equation of second order, Doctoral thesis (1994). Zbl0802.11043

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