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THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY
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作者 向建立 严国政 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期339-354,共16页
We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and... We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method. 展开更多
关键词 interior transmission eigenvalue anisotropic medium partially coated boundary the analytic fredholm theory T-coercive method
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Fast Solvers of Fredholm Optimal Control Problems
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作者 Mario Annunziato Alfio Borzi 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第4期431-448,共18页
The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of ... The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments. 展开更多
关键词 Optimal control theory fredholm integral equations of second kind iterative methods
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THE BOUNDARY INTEGRAL METHOD FOR THE HELMHOLTZ EQUATION WITH CRACKS INSIDE A BOUNDED DOMAIN 被引量:3
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作者 郭军 范丽丽 严国政 《Acta Mathematica Scientia》 SCIE CSCD 2015年第3期539-551,共13页
We consider a kind of scattering problem by a crack F that is buried in a bounded domain D, and we put a point source inside the domain D. This leads to a mixed boundary value problem to the Helmholtz equation in the ... We consider a kind of scattering problem by a crack F that is buried in a bounded domain D, and we put a point source inside the domain D. This leads to a mixed boundary value problem to the Helmholtz equation in the domain D with a crack Г. Both sides of the crack F are given Dirichlet-impedance boundary conditions, and different boundary condition (Dirichlet, Neumann or Impedance boundary condition) is set on the boundary of D. Applying potential theory, the problem can be reformulated as a system of boundary integral equations. We establish the existence and uniqueness of the solution to the system by using the Fredholm theory. 展开更多
关键词 Boundary integral equation Helmholtz equation fredholm theory
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TOEPLITZ OPERATORS ON HEISENBERG GROUP
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作者 谢佩珠 曹广福 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1589-1597,共9页
Denote by Ω the Siegel domain in Cn, n 〉 1. In this paper, we study the essential spectra of Toeplitz operators defined on the Hardy space H2(а↓Ω). In addition, the characteristic equation of analytic Toeplitz ... Denote by Ω the Siegel domain in Cn, n 〉 1. In this paper, we study the essential spectra of Toeplitz operators defined on the Hardy space H2(а↓Ω). In addition, the characteristic equation of analytic Toeplitz operators iааs obtained. 展开更多
关键词 Toeplitz operator Hardy space fredholm theory
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Solitary Wave Solutions of Delayed Coupled Higgs Field Equation
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作者 Shu Guan JI Xiao Wan LI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2022年第1期97-106,共10页
This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of s... This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|^(2)-2uv-τu(|u|^(2))x=0 vtt+vxx-β(|u|^(x))xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation. 展开更多
关键词 delayed coupled Higgs field equation solitary wave solutions geometric singular perturbation theory fredholm theory homoclinic orbit
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Toeplitz operators on H^2(iR)
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作者 XIE PeiZhu CAO GuangFu 《Science China Mathematics》 SCIE 2011年第9期1995-2004,共10页
In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is... In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed. 展开更多
关键词 Toeplitz operator Hardy space fredholm theory
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