Analytic and Gevrey Well-Posedness of the Cauchy Problem for Second Order Weakly Hyperbolic Equations with Coefficients Irregular in Time

1986 ◽  
pp. 363-380 ◽  
Author(s):  
Sergio SPAGNOLO
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Well Posedness ◽  
The Cauchy Problem

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

scholarly journals Well-Posedness of the Cauchy Problem for Hyperbolic Equations with Non-Lipschitz Coefficients

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
Akbar B. Aliev ◽  
Gulnara D. Shukurova
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Well Posedness ◽  
Singular Coefficients ◽  
The Cauchy Problem ◽  
Finite Smoothness

We consider hyperbolic equations with anisotropic elliptic part and some non-Lipschitz coefficients. We prove well-posedness of the corresponding Cauchy problem in some functional spaces. These functional spaces have finite smoothness with respect to variables corresponding to regular coefficients and infinite smoothness with respect to variables corresponding to singular coefficients.

HOMOGENEOUS HYPERBOLIC EQUATIONS WITH COEFFICIENTS DEPENDING ON ONE SPACE VARIABLE

2007 ◽  
Vol 04 (03) ◽  
pp. 533-553 ◽  
Author(s):  
SERGIO SPAGNOLO ◽  
GIOVANNI TAGLIALATELA
Keyword(s):  
Cauchy Problem ◽  
Space Variable ◽  
Hyperbolic Equations ◽  
Diagonal Matrix ◽  
Well Posedness ◽  
Characteristic Roots ◽  
The Cauchy Problem

We investigate the Cauchy problem for homogeneous equations of order m in the (t,x)-plane, with coefficients depending only on x. Assuming that the characteristic roots satisfy the condition [Formula: see text] we succeed in constructing a smooth symmetrizer which behaves like a diagonal matrix: this allows us to prove the well-posedness in [Formula: see text].

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