In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certa...In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.展开更多
The following inverse problem is solved—given the eigenvalues and the potential b(n) for a difference boundary value problem with quadratic dependence on the eigenparameter, λ, the weights c(n) can be uniquely ...The following inverse problem is solved—given the eigenvalues and the potential b(n) for a difference boundary value problem with quadratic dependence on the eigenparameter, λ, the weights c(n) can be uniquely reconstructed. The investi-gation is inductive on m where represents the number of unit intervals and the results obtained depend on the specific form of the given boundary conditions. This paper is a sequel to [1] which provided an algorithm for the solution of an analogous inverse problem, where the eigenvalues and weights were given and the potential was uniquely reconstructed. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in [1], an additional spectrum is required more often than was the case in [1].展开更多
In this paper,a class of inverse boundary value problems for(λ,1)bi-analytic functions is given.Using the method of Riemann boundary value problem for analytic functions,the conditions of solvability and the expressi...In this paper,a class of inverse boundary value problems for(λ,1)bi-analytic functions is given.Using the method of Riemann boundary value problem for analytic functions,the conditions of solvability and the expression of the solutions for the inverse problems are obtained.展开更多
We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of bounda...We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems.展开更多
For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of uni...For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field.The models created in this way are particularly satisfactory for a high_speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.展开更多
A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first...A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.展开更多
文摘In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.
文摘The following inverse problem is solved—given the eigenvalues and the potential b(n) for a difference boundary value problem with quadratic dependence on the eigenparameter, λ, the weights c(n) can be uniquely reconstructed. The investi-gation is inductive on m where represents the number of unit intervals and the results obtained depend on the specific form of the given boundary conditions. This paper is a sequel to [1] which provided an algorithm for the solution of an analogous inverse problem, where the eigenvalues and weights were given and the potential was uniquely reconstructed. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in [1], an additional spectrum is required more often than was the case in [1].
基金Supported by the Natural Science Foundation of Fujian Province(2020J01322)
文摘In this paper,a class of inverse boundary value problems for(λ,1)bi-analytic functions is given.Using the method of Riemann boundary value problem for analytic functions,the conditions of solvability and the expression of the solutions for the inverse problems are obtained.
基金supported by the National Natural Science Foundation of China (Grant No. 10671046)
文摘We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems.
文摘For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field.The models created in this way are particularly satisfactory for a high_speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.
基金Supported by the National Natural Science Foundation of China (Grant No. 40374001)
文摘A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.
