scholarly journals Cauchy problem in Gevrey classes for non-strictly hyperbolic equations of second order

1977 ◽  
Vol 17 (3) ◽  
pp. 513-531
Author(s):  
Katsuju Igari
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Gevrey Classes

Nonlocal and Initial Problems for Quasilinear, Nonstrictly Hyperbolic Equations with General Solutions Represented by Superposition of Arbitrary Functions

2003 ◽  
Vol 10 (4) ◽  
pp. 687-707
Author(s):  
J. Gvazava
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Quasilinear Equations ◽  
General Solutions ◽  
Parabolic Degeneracy

Abstract We have selected a class of hyperbolic quasilinear equations of second order, admitting parabolic degeneracy by the following criterion: they have a general solution represented by superposition of two arbitrary functions. For equations of this class we consider the initial Cauchy problem and nonlocal characteristic problems for which sufficient conditions are established for the solution solvability and uniquness; the domains of solution definition are described.

scholarly journals On the Cauchy problem for finitely degenerate hyperbolic equations of second order

2000 ◽  
Vol 38 (2) ◽  
pp. 223-230 ◽  
Author(s):  
Ferruccio Colombini ◽  
Haruhisa Ishida ◽  
Nicola Orrú
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Second Order ◽  
The Cauchy Problem ◽  
Degenerate Hyperbolic Equations
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