Analytic solutions to nonlocal abstract equations

Marina Ghisi

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 1, page 181-198
  • ISSN: 0392-4041

Abstract

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In this paper we study the problem of existence of global solutions for some classes of abstract equations, that generalize some type of Klein-Gordon equations, with nonlinear nonlocal terms of Kirchhoff type. We find some conditions that guarantee the existence of such solutions whether in presence or in absence of a conserved energy.

How to cite

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Ghisi, Marina. "Analytic solutions to nonlocal abstract equations." Bollettino dell'Unione Matematica Italiana 6-B.1 (2003): 181-198. <http://eudml.org/doc/195652>.

@article{Ghisi2003,
abstract = {In this paper we study the problem of existence of global solutions for some classes of abstract equations, that generalize some type of Klein-Gordon equations, with nonlinear nonlocal terms of Kirchhoff type. We find some conditions that guarantee the existence of such solutions whether in presence or in absence of a conserved energy. },
author = {Ghisi, Marina},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {181-198},
publisher = {Unione Matematica Italiana},
title = {Analytic solutions to nonlocal abstract equations},
url = {http://eudml.org/doc/195652},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Ghisi, Marina
TI - Analytic solutions to nonlocal abstract equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/2//
PB - Unione Matematica Italiana
VL - 6-B
IS - 1
SP - 181
EP - 198
AB - In this paper we study the problem of existence of global solutions for some classes of abstract equations, that generalize some type of Klein-Gordon equations, with nonlinear nonlocal terms of Kirchhoff type. We find some conditions that guarantee the existence of such solutions whether in presence or in absence of a conserved energy.
LA - eng
UR - http://eudml.org/doc/195652
ER -

References

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  2. AROSIO, A.- SPAGNOLO, S., Global existence for abstract evolution equations of weakly hyperbolic type, J. Math. Pures et Appl., 65 (1986), 263-305. Zbl0616.35049MR875159
  3. BERNSTEIN, S., Sur une classe d'équations fonctionelles aux dérivées partielles, Izv. Akad. Nauk. SSSR, Sér Math., 4 (1940), 17-26. Zbl0026.01901MR2699
  4. COLOMBINI, F.- DE GIORGI, E.- SPAGNOLO, S., sur les équations hyperboliques avec des coefficients qui ne dépendent que du temps, Ann. Sc. Norm. Sup. Pisa, 6 (1979), 511-559. Zbl0417.35049MR553796
  5. D'ANCONA, P.- SPAGNOLO, S., Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math., 108 (1992), 247-262. Zbl0785.35067MR1161092
  6. D'ANCONA, P.- SPAGNOLO, S., On an abstract weakly hyperbolic equation modeling the nonlinear vibrating string, Developments in Partial Differential Equations and Applications to Mathematical Physic, Edited by G. Buttazzo et. al. Plenum Press, New-York1992. Zbl0898.35103MR1213920
  7. GHISI, M.- SPAGNOLO, S., Global analytic solutions to hyperbolic systems, NODEA, 5 (1998), 245-264. Zbl0904.35048MR1618978
  8. KIRCHHOFF, G., «Vorlesurngen über Mechanik» Teubner, Leipzig1883. JFM08.0542.01
  9. POHOZAEV, S. I., On a class of quasilinear hyperbolic equations, Mat. Sbornik, 96 (138) (1975) No. 1, 152-166 (Trans. Math. USSR Sbornik, 25 (1975) No. 1). Zbl0328.35060MR369938
  10. SPAGNOLO, S., The Cauchy problem for the Kirchhoff equations, Rend. Sem. Fisico Matematico di Milano, 62 (1992), 17-51. Zbl0809.35061MR1293773

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