scholarly journals Gevrey wellposedness of the Cauchy problem for the hyperbolic equations of third order with coefficients depending only on time

1998 ◽  
Vol 34 (3) ◽  
pp. 249-270 ◽  
Author(s):  
Tamotu Kinoshita
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Third Order ◽  
The Cauchy Problem

scholarly journals Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

2020 ◽  
Vol 12 (2) ◽  
pp. 419-433
Author(s):  
O.M. Buhrii ◽  
O.T. Kholyavka ◽  
P.Ya. Pukach ◽  
M.I. Vovk
Keyword(s):  
Cauchy Problem ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Lebesgue Spaces ◽  
Third Order ◽  
The Third ◽  
The Cauchy Problem

We investigate weak solutions of the Cauchy problem for the third order hyperbolic equations with variable exponent of the nonlinearity. The problem is considered in some classes of functions namely in Lebesgue spaces with variable exponents. The sufficient conditions of the existence and uniqueness of the weak solutions to given problem are found.

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.

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