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THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

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Acta Mathematica Scientia 2024年第3期44卷 973-983页

作者：肖存涛邱华姚正安 School of Mathematics and Statistics Guangdong University of TechnologyGuangzhou510090China Department of Mathematics South China Agricultural UniversityGuangzhou510642China School of Mathematics Sun Yat-sen UniversityGuangzhou510275China

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small in... 详细信息

关键词： regularized MHD equations fractional Laplacian global well-posedness analyticity decay rate

decay rate of Solutions to Hyperbolic System of First Order

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Acta Mathematica Sinica,English Series 1999年第4期15卷 471-484页

作者： Shuxing Chen Yi Zhou Institute of Mathematics,Fudan University,Shanghai 200433,P.R.China E-mail:sxchen@*** Fax:021-65646073 Institute of Mathematics Fudan University Shanghai P. R. China

In this paper we generalize the global Sobolev inequality introduced by Klainerman in studying wave equation to the hyperbolic system case.We obtain several decay estimates of solutions of a hyperbolic system of first order by different norms of initial data.In particular,the result mentioned in Theorem 1.5 offers an optimal decay rate of solutions,if the initial data belongs to the assigned weighted Sobolev space.In the proof of the theorem we reduce the estimate of solutions of a hyperbolic system to the corresponding case for a scalar pseudodifferential equation of the first order,and then establish the required estimate by using microlocal analysis.

关键词： Hyperbolic system decay rate Asymptotic behaviour Microlocal analysis

decay rate of Larix gmelinii coarse woody debris on burned patches in the Greater Khingan Mountains

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Journal of Forestry Research 2021年第6期32卷 2349-2363页

作者： Shubo Huang Lixiang Wen Shuai Yin Meng Guo Fangbing Yu Key Laboratory of Geographical Processes and Ecological Security in Changbai Mountains School of Geographical SciencesNortheast Normal UniversityMinistry of EducationChangchun130024People’s Republic of China Center for Global Environmental Research National Institute for Environmental StudiesTsukuba3058506Japan

The decomposition of coarse woody debris(CWD)affects the energy flow and nutrient cycling in forest ecosystems.Previous studies on CWD have focused on the input,decomposition,reserve dynamics,and CWD functions,but coarse woody debris decomposition is complex and the results from different regions vary considerably.It is not clear which factors affect decay rate(k),especially at different decomposition stages.In this study,a single-exponential decay model was used to analyze the characteristics of CWD decomposition in Larix gmelinii forests over the 33 years following a fire in the Greater Khingan Mountains.The results show that the decay rate of coarse woody debris was positively correlated to decay class.The average decomposition rate was 0.019,and 41 years and 176 years are needed for a 50%and 95%mass loss,respectively.CWD nutrient content,density,and water content could explain the variance in the decay rate(~42%)of the decay factors such as amount of leaching,degree of fragmentation,respiration of the debris,and biotransformation,and varied significantly between different decay classes.Using the space-time substitution method,this study arranged the coarse woody debris of different mortality times to form a 33 year chronosequence which revealed the decomposition process.It was concluded that the decay rate was mainly explained by structural component of the debris and its nitrogen and water contents.This paper quantifies the indicators affecting CWD decay to explain the decomposition process.

关键词： Coarse woody debris decay rate Space–time substitution Boreal forest Fire disturbance

decay rate OF SAINT-VENANT END EFFECTS FOR PLANE DEFORMATIONS OF PIEZOELECTRIC-PIEZOMAGNETIC SANDWICH STRUCTURES

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Acta Mechanica Solida Sinica 2010年第5期23卷 407-419页

作者： Yan Xue Jinxi Liu Institutes of Engineering Mechanics Beijing Jiaotong University Beijing 100044 China Department of Engineering Mechanics Shijiazhuang Tiedao University Shijiazhuang 050043 China

This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric （PE）-piezomagnetic （PM） sandwich structures, where a PM layer is located between two PE layers with the same material properties or reversely. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lower surfaces of the sandwich structure axe mechanically free, electrically open or shorted as well as magnetically open or shorted. Firstly the constitutive equations of PE mate- rials and PM materials for plane strain are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into differential equations in a matrix form. Finally, by using the transfer matrix method, the characteristic equations for eigen- values or decay rates axe derived. Based on the obtained characteristic equations, the decay rates for the PE-PM-PE and PM-PE-PM sandwich structures are calculated. The influences of the electromagnetic boundary conditions, material properties of PE layers and volume fraction on the decay rates are discussed in detail.

关键词： Saint-Venant＇s principle decay rate end effect piezoelectric material piezomag- netic material sandwich structure plane deformation

decay rate FOR DEGENErate CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS

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Acta Mathematica Scientia 2015年第2期35卷 281-302页

作者：陆云光 Christian KLINGENBERG Ujjwal KOLEY Xuezhou LU Department of Mathematics Hangzhou Normal University Institut fur Mathematik Julius-Maximilians-Universitat Wiirzburg Laboratoire Ondes and Milieux Complexes UMR 6294 CNRS-Universite du Havre

We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.

关键词： Degenerate convection-diffusion equations regularity decay rate Lax-Oleinik type inequality

decay rate of Quasilinear Wave Equation with Viscosity

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 591-596页

作者： Yu-ming QIN Xin LIU Shu-xian DENG Department of Applied Mathematics College of SciencesDonghua UniversityShanghai 201620China College of Information Sciences and Technology Donghua UniversityShanghai 201620China

This paper is concerned with the decay rate of solutions for a quasilinear wave equation with viscosity. We use a so-called energy perturbation method to establish decay rate of solutions in terms of energy norm for a class of nonlinear functions. With the help of a comparison lemma of differential inequalities, we establish a relationship between decay rate of solutions and f.

关键词： decay rate energy inequality quasilinear wave equation

decay rate OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES

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Acta Mathematica Scientia 2017年第6期37卷 1607-1618页

作者：高翔马际华 School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1 ≤ξ 〈 θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ = θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ ahaost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

关键词： self-similar measures Fourier transforms decay rate normal numbers

Rational Energy decay rate of a Wave Equation: the Case of Dimension ≥ 2

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Journal of Applied Mathematics and Physics 2022年第10期10卷 2851-2855页

作者： Rabba Idi Yacouba Strasbourg University Strasbourg France

We apply the multiplier method to obtain the rational energy decay rate of the energy of wave equation in case n ≥ 2, under an assumption on the potential energy.

关键词： Wave Equation decay rate Multiplier Method

An Analysis of the decay rate of Combustion Gases in U.S. Homes Using Unvented Gas Fireplaces

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An Analysis of the Decay Rate of Combustion Gases in U.S. Ho...