scholarly journals On the Cauchy Problem for Second-Order Hyperbolic Operators with the Coefficients of Their Principal Parts Depending Only on the Time Variable

2012 ◽  
Vol 55 (1) ◽  
pp. 99-136 ◽  
Author(s):  
Seiichiro Wakabayashi
Keyword(s):  
Cauchy Problem ◽  
Second Order ◽  
Time Variable ◽  
Hyperbolic Operators ◽  
The Cauchy Problem ◽  
Principal Parts

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.

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