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 Integrated cosine functions

1996 ◽  
Vol 19 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Quan Zheng
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Second Order ◽  
Basic Theory ◽  
Cosine Function ◽  
Integrated Semigroups ◽  
Approximation Theorems ◽  
The Relationship ◽  
Cosine Functions

In order to the second order Cauchy problem(CP2):x″(t)=Ax(t),x(0)=x∈D(An),x″(0)=y∈D(Am)on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

scholarly journals Find A General Solution Of An Equation Of The Hyperbolic Type With A Second-Order Singular Coefficient And Solve The Cauchy Problem Posed For This Equation.

2021 ◽  
Vol 25 (1) ◽  
pp. 80
Author(s):  
Karimova Shalola Musayevna ◽  
Melikuzieva Dilshoda Mukhtorjon qizi
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Type Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Singular Coefficient ◽  
The Cauchy Problem

This paper presents a general solution of a hyperbolic type equation with a second-order singular coefficient and a solution to the Cauchy problem posed for this equation.

scholarly journals An iterative method for the Cauchy problem for second-order elliptic equations

2018 ◽  
Vol 142-143 ◽  
pp. 216-223 ◽  
Author(s):  
George Baravdish ◽  
Ihor Borachok ◽  
Roman Chapko ◽  
B. Tomas Johansson ◽  
Marián Slodička
Keyword(s):  
Cauchy Problem ◽  
Iterative Method ◽  
Elliptic Equations ◽  
Second Order ◽  
The Cauchy Problem ◽  
Second Order Elliptic Equations
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