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LOCAL REGULARITY FOR SOLUTIONS TO QUASI-LINEAR SINGULAR PARABOLIC EQUATIONS WITH ANISOTROPIC WEIGHTS

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arXiv 2023年

作者： Miao, Changxing Zhao, Zhiwen Beijing Computational Science Research Center Beijing100193 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China

This paper develops a concise procedure for the study on local behavior of solutions to anisotropically weighted quasi-linear singular parabolic equations of p-Laplacian type, which is realized by improving the energy inequalities and applying intrinsic scaling factor to the De Giorgi truncation method. In particular, it also presents a new proof for local Hölder continuity of the solution in the unweighted case. Copyright © 2023, The Authors. All rights reserved.

关键词： Partial differential equations

Parareal Algorithms for Stochastic Maxwell Equations Driven by Multiplicative Noise

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arXiv 2025年

作者： Zhang, Liying Zhang, Qi Ji, Lihai School of Mathematical Science China University of Mining and Technology Beijing100083 China Institute of Applied Physics and Computational Mathematics Beijing100094 China Shanghai Zhangjiang Institute of Mathematics Shanghai201203 China

This paper investigates the parareal algorithms for solving the stochastic Maxwell equations driven by multiplicative noise, focusing on their convergence, computational efficiency and numerical performance. The algorithms use the stochastic exponential integrator as the coarse propagator, while both the exact integrator and the stochastic exponential integrator are used as fine propagators. Theoretical analysis shows that the mean square convergence rates of the two algorithms selected above are proportional to k/2, depending on the iteration number of the algorithms. Numerical experiments validate these theoretical findings, demonstrating that larger iteration numbers k improve convergence rates, while larger damping coefficients σ accelerate the convergence of the algorithms. Furthermore, the algorithms maintain high accuracy and computational efficiency, highlighting their significant advantages over traditional exponential methods in long-term simulations. Copyright © 2025, The Authors. All rights reserved.

关键词： Maxwell equations

Infinitely Many Non-Conservative Solutions for the Three-Dimensional Euler Equations with Arbitrary Initial Data in C1 / 3 −Ε

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SSRN

SSRN 2023年

作者： Khor, Calvin Miao, Changxing Ye, Weikui Beijing Computational Science Research Center Beijing100193 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China

关键词： Euler equations

Magnetic transition in marcasite FeTe2 induced by the competition between crystal field splitting and Coulomb repulsion

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arXiv 2025年

作者： Hou, Yue-Fei Shao, Zhibin Pan, Minghu Wu, Shiyang Zheng, Fawei Fu, Zhen-Guo Zhang, Ping Institute of Applied Physics and Computational Mathematics Beijing100088 China Graduate School China Academy of Engineering Physics Beijing100088 China Physics Laboratory Industrial Training Center Shenzhen Polytechnic University Shenzhen518055 China School of Physics and Information Technology Shaanxi Normal University Xi’an710119 China School of Physics Beijing Institute of Technology Beijing100081 China National Key Laboratory of Computational Physics Beijing100088 China School of Physics and Physical Engineering Qufu Normal University Qufu273165 China

The magnetic ground states in crystalline systems are significant for both fundamental condensed matter physics and practical materials engineering. Marcasite FeTe2, characterized as a small-gap semiconductor, exhibits anomalous magnetic behaviors in low-temperature experiments. In this study, first-principles density functional theory calculations combined with scanning tunneling microscopy/spectroscopy are employed to investigate the magnetic ground state of marcasite FeTe2. It is revealed that the competition between crystal field splitting and Coulomb repulsion plays the key role in the formation of localized magnetic moments in FeTe2. The ground state of FeTe2 bulk is confirmed to be nonmagnetic, while the previously observed magnetic responses of FeTe2 are suggested to be related to the magnetic Fe atoms on the crystal surfaces. Our work proposes a straightforward theoretical criterion for determining ground-state magnetism of various localized-moment systems. © 2025, CC BY.

关键词： Magnetic moments

Sharp restriction estimates for several degenerate higher co-dimensional quadratic surfaces

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arXiv 2024年

作者： Cao, Zhenbin Miao, Changxing Pang, Yixuan Institute of Mathematics Henan Academy of Sciences Zhengzhou450046 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Mathematics University of Pennsylvania PhiladelphiaPA19104 United States

Fourier restriction conjecture is an important problem in harmonic analysis. Guo-Oh in [17] studied the restriction estimates for quadratic surfaces of co-dimension 2 in R5. For one special surface (ξ1, ξ2, ξ3, ξ12, ξ22 + ξ1ξ3), they applied a nested induction argument to build essentially sharp restriction estimate. In this paper, we simplify their method, and extend it to a variant of the broad-narrow analysis. As applications, we will prove essentially sharp restriction estimates for some kinds of degenerate higher co-dimensional quadratic surfaces. Copyright © 2024, The Authors. All rights reserved.

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An Improved Hybrid Method for Solving Large-Scale Electromagnetic Problems with Local Inhomogeneous Structures

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An Improved Hybrid Method for Solving Large-Scale Electromag...

International applied computational Electromagnetics Society Symposium (ACES)

作者： Yang Liu Chao-Fu Wang Wen-Bin Wu Hai-Jing Zhou Institute of Applied Physics and Computational Mathematics Beijing P. R. China National University of Singapore Singapore

An iterative FEBI-PO hybrid method has been proposed to deal with the large-scale problem having local inhomogeneous structures. In this paper, the PEC part of exterior surface of inhomogeneous structure is also taken as PO region, which makes the PO region as large as possible. Moreover, in the iterative process, only the problem with the variables on the dielectric boundary of local complex inhomogeneous structure and the problem with variables in PO region need to be solved alternately, which avoids solving the whole problem in FEBI region repeatedly. In addition, several numerical results are discussed to illuminate the efficiency of the improved scheme.

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Stochastic positivity-preserving symplectic splitting methods for stochastic Lotka–Volterra predator-prey model

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arXiv 2025年

作者： Zhang, Liying Kang, Xinyue Ji, Lihai School of Mathematical Science China University of Mining and Technology Beijing100083 China Institute of Applied Physics and Computational Mathematics Beijing100094 China Shanghai Zhangjiang Institute of Mathematics Shanghai201203 China

In this paper, we present two stochastic positive-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model driven by a multiplicative noise. To inherit the intrinsic characteristic of the original system, the stochastic Lie–Trotter splitting method and the stochastic Strang splitting method are introduced, which are proved to preserve the positivity of the numerical solution and possess the discrete stochastic symplectic conservation law as well. By deriving the uniform boundedness of the p-th moment of the numerical solution, we prove that the strong convergence orders of these two methods are both one in the L2(Ω)norm. Finally, we validate the theoretical results through two and four dimensional numerical examples. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic models

LOCAL BEHAVIOR FOR SOLUTIONS TO ANISOTROPIC WEIGHTED QUASILINEAR DEGENERATE PARABOLIC EQUATIONS

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arXiv 2023年

作者： Miao, Changxing Zhao, Zhiwen Beijing Computational Science Research Center Beijing100193 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China

This paper aims to study the local behavior of solutions to a class of anisotropic weighted quasilinear degenerate parabolic equations with the weights comprising two power-type weights of different dimensions. We first capture the asymptotic behavior of the solution near the singular or degenerate point of the weights. In particular, we find an explicit upper bound on the decay rate exponent determined by the structures of the equations and weights, which can be achieved under certain condition and meanwhile reflects the damage effect of the weights on the regularity of the solution. Furthermore, we prove the local Hölder regularity of solutions to non-homogeneous parabolic p-Laplace equations with single power-type weights. Copyright © 2023, The Authors. All rights reserved.

关键词： Anisotropy

On the global well-posedness of stochastic Schrödinger-Korteweg-de Vries system

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arXiv 2023年

作者： Chen, Jie Gu, Fan Guo, Boling Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Sciences Jimei University Xiamen361021 China

In this paper, we study the global well-posedness of the stochastic S-KdV system in H1()×H1(), which are driven by additive noises. It is difficult to show the global well-posedness of a related perturbation system even for smooth datum and stochastic forces. To overcome it, we introduce a new sequence of approximation equations, which is the key of this paper. We establish priori estimates, global well-posedness and convergences of these approximation equations, which help us to get a pathwise priori estimate of initial *** Codes 60H15, 35Q53, 35Q55 Copyright © 2023, The Authors. All rights reserved.

关键词： Additive noise