Well posedness under Levi conditions for a degenerate second order Cauchy problem

Alessia Ascanelli

Rendiconti del Seminario Matematico della Università di Padova (2007)

  • Volume: 117, page 113-126
  • ISSN: 0041-8994

How to cite

top

Ascanelli, Alessia. "Well posedness under Levi conditions for a degenerate second order Cauchy problem." Rendiconti del Seminario Matematico della Università di Padova 117 (2007): 113-126. <http://eudml.org/doc/108704>.

@article{Ascanelli2007,
author = {Ascanelli, Alessia},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {blow-up; -well posedness; Gevrey-well posedness},
language = {eng},
pages = {113-126},
publisher = {Seminario Matematico of the University of Padua},
title = {Well posedness under Levi conditions for a degenerate second order Cauchy problem},
url = {http://eudml.org/doc/108704},
volume = {117},
year = {2007},
}

TY - JOUR
AU - Ascanelli, Alessia
TI - Well posedness under Levi conditions for a degenerate second order Cauchy problem
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2007
PB - Seminario Matematico of the University of Padua
VL - 117
SP - 113
EP - 126
LA - eng
KW - blow-up; -well posedness; Gevrey-well posedness
UR - http://eudml.org/doc/108704
ER -

References

top
  1. [1] A. ASCANELLI - M. CICOGNANI, Energy estimate and Fundamental Solution for Degenerate Hyperbolic Cauchy problems. J. Differential Equations, 217 (2005), pp. 305-340. Zbl1087.35066MR2168825
  2. [2] A. ASCANELLI - M. CICOGNANI, Well posedness of the Cauchy problem for some degenerate hyperbolic operators. Pseudo-Differential Operators and Related Topics, Series: Operator Theory: Advances and Applications, Vol. 164, Editors: P. Boggiatto, L. Rodino, J. Toft, M.-W. Wong, Birkhuser Verlag Basel/Switzerland (2006), pp. 23-41. Zbl1101.35058MR2243964
  3. [3] M. D. BRONSÏTEǏN, The Cauchy problem for hyperbolic operators with characteristics of variable multiplicity. Trudy Moskov. Mat. Obshch. 41 (1980), pp. 83-99. Zbl0468.35062MR611140
  4. [4] M. CICOGNANI, The Cauchy problem for strictly hyperbolic operators with non-absolutely continuous coefficients. Tsukuba J. Math. 27 (2003), pp. 1-12. Zbl1041.35049MR1999231
  5. [5] M. CICOGNANI, Coefficients with unbounded derivatives in hyperbolic equations. Math. Nachr. 277 (2004), pp. 1-16. Zbl1060.35071MR2100045
  6. [6] F. COLOMBINI - E. DE GIORGI - S. SPAGNOLO, Sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps. Ann. Sc. Norm. Sup. Pisa 6 (1979), pp. 511-559. Zbl0417.35049MR553796
  7. [7] F. COLOMBINI - D. DEL SANTO - T. KINOSHITA, Well posedness of the Cauchy problem for a hyperbolic equation with non-Lipschitz coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1 (2002), pp. 327-358. Zbl1098.35094MR1991143
  8. [8] F. COLOMBINI - D. DEL SANTO - M. REISSIG, On the optimal regularity coefficients in hyperbolic Cauchy problem, Bull. Sci. Math. 127 (2003), pp. 328-347. Zbl1037.35038MR1988632
  9. [9] F. COLOMBINI - H. ISHIDA - N. ORRU, On the Cauchy problem for finitely degenerate hyperbolic equations of second order. Ark. Mat. 38 (2000), pp. 223-230. Zbl1073.35145MR1785400
  10. [10] F. COLOMBINI - E. JANNELLI - S. SPAGNOLO, Well posedness in Gevrey classes of the Cauchy problem for a non strictly hyperbolic equation with coefficients depending on time. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10 (1983), pp. 291-312. Zbl0543.35056MR728438
  11. [11] F. COLOMBINI - T. NISHITANI, On finitely degenerate hyperbolic operators of second order. Osaka J. Math. 41, 4 (2004) pp. 933-947. Zbl1068.35078MR2116346
  12. [12] V. JA IVRIǏ, Conditions for correctness in Gevrey classes of the Cauchy problem for hyperbolic operators with characteristics of variable multiplicity. (Russian) Sibirsk. Mat. ZÏ. 17 (1976), pp. 1256-1270. Zbl0352.35060MR454368
  13. [13] K. KAJITANI, Cauchy problem for nonstrictly hyperbolic systems in Gevrey classes. J. Math. Kyoto Univ. 23-3 (1983), pp. 599-616. Zbl0544.35063MR721386
  14. [14] A. KUBO - M. REISSIG, Construction of parametrix for hyperbolic equations with fast oscillations in non-Lipschitz coefficients. Comm. Partial Differential Equations 28 (2003), pp. 1471-1502. Zbl1036.35118MR1998944
  15. [15] S. MIZOHATA, On the Cauchy problem. Notes and Reports in Mathematics in Science and Engineering, 3. Academic Press, Inc., Orlando, FL; Science Press, Beijing, 1985. Zbl0616.35002MR860041
  16. [16] T. NISHITANI, The Cauchy problem for weakly hyperbolic equations of second order. Comm. Partial Differential Equations, 5 (1980), pp. 1273-1296. Zbl0497.35053MR593968

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.