Well-posedness of the cauchy problem in gevrey classes for some weakly hyperbolic equations of higher order

2003 ◽  
Vol 90 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Ferruccio Colombini ◽  
Haruhisa Ishida
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Higher Order ◽  
Well Posedness ◽  
Gevrey Classes ◽  
The Cauchy Problem

scholarly journals On the wellposedness of the Cauchy problem for weakly hyperbolic equations of higher order

2005 ◽  
Vol 278 (10) ◽  
pp. 1147-1162 ◽  
Author(s):  
Piero D'Ancona ◽  
Tamotu Kinoshita
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Higher Order ◽  
The Cauchy Problem

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].

Well-posedness and limit behaviors for a stochastic higher order modified Camassa–Holm equation

2016 ◽  
Vol 16 (06) ◽  
pp. 1650019
Author(s):  
Lin Lin ◽  
Guangying Lv ◽  
Wei Yan
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Higher Order ◽  
Well Posedness ◽  
Local Existence And Uniqueness ◽  
Holm Equation ◽  
The Cauchy Problem

This paper is devoted to the Cauchy problem for a stochastic higher order modified-Camassa–Holm equation [Formula: see text] The local existence and uniqueness with initial data [Formula: see text], [Formula: see text] and [Formula: see text], is established. The limit behaviors of the solution are examined as [Formula: see text].

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