On the well-posedness of the Cauchy problem for certain hyperbolic operators with characteristics of high variable multiplicity

1982 ◽  
Vol 37 (3) ◽  
pp. 225-226 ◽  
Author(s):  
O V Zaitseva ◽  
V Ya Ivrii
Keyword(s):  
Cauchy Problem ◽  
Well Posedness ◽  
Variable Multiplicity ◽  
Hyperbolic Operators ◽  
The Cauchy Problem

scholarly journals Inhomogeneous Gevrey ultradistributions and Cauchy problem

2006 ◽  
Vol 133 (31) ◽  
pp. 176-186
Author(s):  
Daniela Calvo ◽  
L. Rodino
Keyword(s):  
Cauchy Problem ◽  
Weight Function ◽  
Differential Operators ◽  
Subject Classification ◽  
Well Posedness ◽  
Gevrey Classes ◽  
Partial Differential Operators ◽  
Hyperbolic Operators ◽  
The Cauchy Problem ◽  
Constant Coefficients

After a short survey on Gevrey functions and ultradistributions, we present the inhomogeneous Gevrey ultradistributions introduced recently by the authors in collaboration with A. Morando, cf. [7]. Their definition depends on a given weight function ?, satisfying suitable hypotheses, according to Liess-Rodino [16]. As an application, we define (s, ?)-hyperbolic partial differential operators with constant coefficients (for s > 1), and prove for them the well-posedness of the Cauchy problem in the frame of the corresponding inhomogeneous ultradistributions. This sets in the dual spaces a similar result of Calvo [4] in the inhomogeneous Gevrey classes, that in turn extends a previous result of Larsson [14] for weakly hyperbolic operators in standard homogeneous Gevrey classes. AMS Mathematics Subject Classification (2000): 46F05, 35E15, 35S05.

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