First Darboux problem for nonlinear hyperbolic equations of second order

First Darboux problem for nonlinear hyperbolic equations of second order

We study the first Darboux problem for hyperbolic equations of second order with power nonlinearity. We consider the question of the existence and nonexistence of global solutions to this problem depending on the sign of the parameter before the nonlinear term and the degree of its nonlinearity. We...

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Veröffentlicht in:Mathematical Notes 2008-12, Vol.84 (5-6), p.646-663
Hauptverfasser: Dzhokhadze, O. M., Kharibegashvili, S. S.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:We study the first Darboux problem for hyperbolic equations of second order with power nonlinearity. We consider the question of the existence and nonexistence of global solutions to this problem depending on the sign of the parameter before the nonlinear term and the degree of its nonlinearity. We also discuss the question of local solvability of the problem.
ISSN:0001-4346
1573-8876
DOI:10.1134/S0001434608110060