On the existence and absence of global solutions of the first Darboux problem for nonlinear wave equations

On the existence and absence of global solutions of the first Darboux problem for nonlinear wave equations

For the one-dimensional wave equation with a power-law nonlinearity, we consider the first Darboux problem, for which we study issues related to the existence and absence of local and global solutions.

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Veröffentlicht in:Differential equations 2008-03, Vol.44 (3), p.374-389
Hauptverfasser: Berikelashvili, G. K., Dzhokhadze, O. M., Midodashvili, B. G., Kharibegashvili, S. S.
Format: Artikel
Sprache:eng
Schlagworte:
Difference and Functional Equations
Inequality
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Studies
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Beschreibung
Zusammenfassung:For the one-dimensional wave equation with a power-law nonlinearity, we consider the first Darboux problem, for which we study issues related to the existence and absence of local and global solutions.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266108030087