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Numerical Identification of nonlocal potentials in Aggregation

Communications in Computational Physics 2022年第8期32卷 638-670页

作者： Yuchen He Sung Ha Kang Wenjing Liao Hao Liu Yingjie Liu Institute of Natural Sciences Shanghai Jiao Tong UniversityShanghaiChina School of Mathematics Georgia Institute of TechnologyAtlantaGeorgiaGA 30332-0160USA Department of Mathematics Hong Kong Baptist UniversityHong Kong SAR

Aggregation equations are broadly used tomodel population dynamicswith nonlocal interactions,characterized by a potential in the *** paper considers the inverse problem of identifying the potential from a single noisy spatialtemporal *** identification is challenging in the presence of noise due to the instability of numerical *** propose a robust model-based technique to identify the potential by minimizing a regularized data fidelity term,and regularization is taken as the total variation and the squared Laplacian.A split Bregman method is used to solve the regularized optimization *** method is robust to noise by utilizing a Successively Denoised Differentiation *** consider additional constraints such as compact support and symmetry constraints to enhance the performance *** also apply thismethod to identify time-varying potentials and identify the interaction kernel in an agent-based *** numerical examples in one and two dimensions are included to verify the effectiveness and robustness of the proposed method.

关键词： Aggregation equation nonlocal potential PDE identification Bregman iteration operator splitting

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Estimates on the eigenvalues of complex nonlocal Sturm-Liouville problems

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Applied Mathematics(A Journal of Chinese Universities) 2023年第1期38卷 100-110页

作者： SUN Fu LI Kun School of Statistics and Data Science Qufu Normal UniversityQufu 273165China School of Mathematical Sciences Qufu Normal UniversityQufu 273165China School of Mathematics and Statistics Shandong UniversityWeihai 264209China

The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value *** bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.

关键词： Sturm-Liouville problem nonlocal potential complex valued coefficient non-real eigenvalue

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