Let S be the surface of the earth, S<sub>1</sub> its part occupied by land, S<sub>2</sub> its part by sea, andr means a distance of a variable point to the geocenter. As a new kind of geodeticb...Let S be the surface of the earth, S<sub>1</sub> its part occupied by land, S<sub>2</sub> its part by sea, andr means a distance of a variable point to the geocenter. As a new kind of geodeticboundary value problem （BVP）, the mixed BVP with respect to disturbing potential展开更多
The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step o...The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.展开更多
A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathe...A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev's spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes' problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case of the GOBVP is also dealt with.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Let S be the surface of the earth, S<sub>1</sub> its part occupied by land, S<sub>2</sub> its part by sea, andr means a distance of a variable point to the geocenter. As a new kind of geodeticboundary value problem （BVP）, the mixed BVP with respect to disturbing potential
基金Project supported by the National Natural Science Foundaion of China.
文摘The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.
基金Project supported by the National Natural Science Foundation of China.
文摘A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev's spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes' problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case of the GOBVP is also dealt with.
