scholarly journals Solution of the Cauchy problem and the mixed problem for degenerating second order hyperbolic equations by the method of finite differences

1968 ◽  
Vol 093 (2) ◽  
pp. 148-157
Author(s):  
Jiří Kopáček
Keyword(s):  
Cauchy Problem ◽  
Mixed Problem ◽  
Finite Differences ◽  
Hyperbolic Equations ◽  
Second Order ◽  
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 Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

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
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