In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under m...In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.展开更多
We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integra...We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integral operators,which leads to a non-Hermitian generalized matrix eigenvalue problems.The spectral indicator method(SIM)is then applied to calculate the(complex)eigenvalues.The convergence is proved using the spectral approximation theory for(non-selfadjoint)compact operators.Numerical examples are presented for validation.展开更多
本文研究一类具纯离散谱的非自伴算子,证明了该类算子在弱拓扑意义下可以特征展开的充分必要条件是该类算子是u-标的(u-scalar),又等价于该类算子拟仿射相似于自伴算子.并给出例子,说明其在弱拓扑意义下可以特征展开,但不属于经典的标...本文研究一类具纯离散谱的非自伴算子,证明了该类算子在弱拓扑意义下可以特征展开的充分必要条件是该类算子是u-标的(u-scalar),又等价于该类算子拟仿射相似于自伴算子.并给出例子,说明其在弱拓扑意义下可以特征展开,但不属于经典的标型谱算子(Spectral operator of scalar type).展开更多
We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions[30]and we prove that the principle of limiting absor...We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions[30]and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum.When an additional dissipative or smallness hypothesis is assumed on the potential,we show that the principle of limiting absorption holds at any point of the essential spectrum.展开更多
基金The Major State Basic Research Program (19871051) of China the NNSF (19972039) of China and Yantai University Doctor Foundation (SX03B20).
文摘In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.
文摘We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integral operators,which leads to a non-Hermitian generalized matrix eigenvalue problems.The spectral indicator method(SIM)is then applied to calculate the(complex)eigenvalues.The convergence is proved using the spectral approximation theory for(non-selfadjoint)compact operators.Numerical examples are presented for validation.
文摘本文研究一类具纯离散谱的非自伴算子,证明了该类算子在弱拓扑意义下可以特征展开的充分必要条件是该类算子是u-标的(u-scalar),又等价于该类算子拟仿射相似于自伴算子.并给出例子,说明其在弱拓扑意义下可以特征展开,但不属于经典的标型谱算子(Spectral operator of scalar type).
文摘We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions[30]and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum.When an additional dissipative or smallness hypothesis is assumed on the potential,we show that the principle of limiting absorption holds at any point of the essential spectrum.
