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Acta Mathematica Scientia 2023年第1期43卷 259-288页

作者：韩波 Manseob LEE LMIB of the Ministry of Education School of Mathematical SciencesBeihang UniversityBeijing100191China Department of Marketing Big Data and Mathematics Mokwon UniversityDaejeon35349Korea

In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property i... 详细信息

关键词： flow Perron property hyperbolicity generalized Lipschitz shadowing property structural stability

Globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting collision

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Science China Mathematics 2022年第5期65卷 1029-1064页

作者： Yangyu Kuang Huazhong Tang Center for Applied Physics and Technology HEDPS and LMAMSchool of Mathematical SciencesPeking UniversityBeijing 100871China

This paper continues to derive the globally hyperbolic moment model of arbitrary order for the three-dimensional special relativistic Boltzmann equation with the Anderson-Witting *** method is the model reduction by the operator *** an orthogonal basis of the weighted polynomial space is crucial and built on infinite families of the complicate relativistic Grad type orthogonal polynomials depending on a parameter and the real spherical harmonics instead of the irreducible *** study the properties of those functions carefully,including their recurrence relations,their derivatives with respect to the independent variable and the parameter,and the zeros of the orthogonal *** moment model is proved to be globally hyperbolic and linearly ***,the Lorentz covariance,the quasi-one-dimensional case,and the non-relativistic and ultra-relativistic limits are also studied.

关键词： moment method hyperbolicity special relativistic Boltzmann equation model reduction operator projection

On Holder Dependence of the Parameterized Hartman–Grobman Theorem

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Acta Mathematica Sinica,English Series 2022年第1期38卷 137-147页

作者： Wen Meng ZHANG Peng LIU Xuan LEI School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331P.R.China

The well-known Hartman-Grobman Theorem says that a C~1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphismΦ.For parameterized systems F_(θ),known results show that the corresponding homeomorphismsΦ_(θ)exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameterθ.In this paper,we further extend the results to Holder dependence ofΦ_(θ)onθby Pugh's strategy,but introducing a kind of special Holder norm instead of the usual supremum norm in the proof to control the linear parts of F_(θ).This requires a new Holder linearization result for every F_(θ).

关键词： Holder linearization dependence on parameter hyperbolicity

A Second Main Theorem of Nevanlinna Theory for Closed Subschemes in Subgeneral Position

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Chinese Annals of Mathematics,Series B 2022年第4期43卷 567-584页

作者： Guangsheng YU School of Mathematics and Statistics Ningbo UniversityNingbo 315211ZhejiangChina

In this paper,by using Seshadri constants for subschemes,the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in(weak)subgeneral *** an application of his second main theorem,he obtain a Brody hyperbolicity result for the complement of nef effective *** also give the corresponding Schmidt’s subspace theorem and arithmetic hyperbolicity result in Diophantine approximation.

关键词： Second main theorem In general position Closed subscheme Seshadri constant Schmidt’s subspace theorem hyperbolicity

On Energy Stable Runge-Kutta Methods for the Water Wave Equation and its Simplified Non-Local Hyperbolic Model

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Communications in Computational Physics 2022年第6期32卷 222-258页

作者： Lei Li Jian-Guo Liu Zibu Liu Yi Yang Zhennan Zhou School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai200240P.R.China Department of Mathematics and Department of Physics Duke UniversityDurhamNC 27708USA Department of Mathematics Duke UniversityDurhamNC 27708USA Nanjing Research Institute of Electronics Technology NanjingP.R.China Beijing International Center for Mathematical Research Peking UniversityP.R.China

Although interest in numerical approximations of the water wave equationgrows in recent years, the lack of rigorous analysis of its time discretization inhibits thedesign of more efficient algorithms. In practice of water wave simulations, the tradeoff between efficiency and stability has been a challenging problem. Thus to shed lighton the stability condition for simulations of water waves, we focus on a model simpli-fied from the water wave equation of infinite depth. This model preserves two mainproperties of the water wave equation: non-locality and hyperbolicity. For the constantcoefficient case, we conduct systematic stability studies of the fully discrete approximation of such systems with the Fourier spectral approximation in space and generalRunge-Kutta methods in time. As a result, an optimal time discretization strategy isprovided in the form of a modified CFL condition, i.e. ∆t = O(√∆x). Meanwhile,the energy stable property is established for certain explicit Runge-Kutta *** CFL condition solves the problem of efficiency and stability: it allows numericalschemes to stay stable while resolves oscillations at the lowest requirement, which onlyproduces acceptable computational load. In the variable coefficient case, the convergence of the semi-discrete approximation of it is presented, which naturally connectsto the water wave equation. Analogue of these results for the water wave equationof finite depth is also discussed. To validate these theoretic observation, extensive numerical tests have been performed to verify the stability conditions. Simulations of thesimplified hyperbolic model in the high frequency regime and the water wave equation are also provided.

关键词： Runge-Kutta methods non-locality hyperbolicity

Stable Weakly Shadowable Volume-preserving Systems Are Volume-hyperbolic

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Acta Mathematica Sinica,English Series 2014年第6期30卷 1007-1020页

作者： Mrio BESSA Manseob LEE Sandra VAZ Universidade da Beira Interior Rua Marquês d’vila e Bolama 6201-001 Covilh Portugal Department of Mathematics Mokwon University Daejeon 302-729 Republic of Korea

We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.

关键词： Weak shadowing dominated splitting hyperbolicity

Classification of Special Anosov Endomorphisms of Nil-manifolds

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Acta Mathematica Sinica,English Series 2019年第12期35卷 1871-1890页

作者： Seyed Mohsen MOOSAVI Khosro TAJBAKHSH Department of Mathematics Faculty of Mathematical Sciences Tarbiat Modares University

In this paper we give a classification of special endomorphisms of nil-manifolds:Let f:N/Γ→N/Γbe a covering map of a nil-manifold and denote by A:N/Γ→N/Γthe nil-endomorphism which is homotopic to *** f is a spec... 详细信息

关键词： hyperbolicity Anosov endomorphisms special Anosov endomorphisms TA maps nilmanifolds

DESCRIPTION AND WENO NUMERICAL APPROXIMATION TO NONLINEAR WAVES OF A MULTI-CLASS TRAFFIC FLOW LWR MODEL

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Applied Mathematics and Mechanics(English Edition) 2005年第6期26卷 691-699页

作者：张鹏戴世强刘儒勋 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Department of Mathematics University of Science & Technology of ChinaHefei 230026P.R.China Department of Mathematics University of Science & Technology of China

A strict proof of the hyperbolicity of the multi-class LWR ( Lighthill-Whitham-Richards) traffic flow model, as well as the descriptions on those nonlinear waves characterized in the traffic flow problems were given. They were mainly about the monotonicity of densities across shocks and in rarefactions. As the system had no characteristic decomposition explicitly, a high resolution and higher order accuracy WENO( weighted essentially non-oscillatory) scheme was introduced to the numerical simulation, which coincides with the analytical description.

关键词： hyperbolicity characteristic traffic wave WENO scheme

New Approach to Differential Equations with Countable Impulses

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Acta Mathematicae Applicatae Sinica 2011年第2期27卷 255-262页

作者： Hong-Kun Zhang Jin-Guo Lian Jiong Sun Department of Mathematics and Statistics University of Massachusetts Amherst MA 01003 USA Department of Mathematics Inner Mongolia University Hohhot Inner Mongolia 010021 China

This paper provides a new approach to study the solutions of a class of generalized Jazobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n ＋ 1. A new class of generalized differential operators is defined. We investigate the kernel of the corresponding maximal operators by applying operator theory. It is shown that all nontrivial solutions to the generalized Jacobi equation are hyperbolic, in which there are n dimension solutions with exponential-decaying amplitude.

关键词： countable impulses differential operator hyperbolic Jacobi fields hyperbolicity differential operators