scholarly journals The Effect of Polar Gaps on the Solutions of Gradiometric Boundary Value Problems

2008 ◽  
Vol 43 (3) ◽  
pp. 97-108 ◽  
Author(s):  
M. Eshagh
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
The Other ◽  
Polar Regions ◽  
Satellite Gravity ◽  
Geopotential Coefficients

The Effect of Polar Gaps on the Solutions of Gradiometric Boundary Value ProblemsThe lack of satellite gravity gradiometric data, due to inclined orbit, in the Polar Regions influences the geopotential coefficients obtained from the solutions of gradiometric boundary value problems. This paper investigates the polar gaps effect on these solutions and it presents that the near zero-, first- and second-order geopotential coefficients are weakly determined by the vertical-vertical, vertical-horizontal and horizontal solutions, respectively. Also it shows that the vertical-horizontal solution is more sensitive to the lack of data than the other solutions.

Boundary value problems with data on opposite characteristics for a second-order mixed-hyperbolic equation

2020 ◽  
Vol 20 (3) ◽  
pp. 6-13
Author(s):  
G.A. Balkizov ◽  
Keyword(s):  
Wave Equation ◽  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Wave Operator ◽  
Boundary Value ◽  
Second Order ◽  
The Other ◽  
The Given

Within the framework of this work, solutions of boundary value problems with data on “opposite” (“parallel”) characteristics are found for one mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic Gellerstedt operator in the other part. It is known that problems with data on opposite (parallel) characteristics for the wave equation in the characteristic quadrangle are posed incorrectly. However, as shown in this paper, the solution of similar problems for a mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic Gellerstedt operator with an order of degeneracy in the other part of the domain, under certain conditions on the given functions, exists, is unique and is written explicitly.

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 Boundary value problems for singular second order equations

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Alessandro Calamai ◽  
Cristina Marcelli ◽  
Francesca Papalini
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Second Order Equations
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