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The Derivation of the Compressible Euler Equation from Quantum Many-Body Dynamics 被引量:1
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作者 Xuwen Chen Shunlin Shen +1 位作者 Jiahao Wu Zhifei Zhang 《Peking Mathematical Journal》 CSCD 2024年第1期35-90,共56页
We study the three-dimensional many-particle quantum dynamics in mean-field set-ting.We forge together the hierarchy method and the modulated energy method.We prove rigorously that the compressible Euler equation is t... We study the three-dimensional many-particle quantum dynamics in mean-field set-ting.We forge together the hierarchy method and the modulated energy method.We prove rigorously that the compressible Euler equation is the limit as the particle num-ber tends to infinity and the Planck’s constant tends to zero.We improve the previous sufficient small time hierarchy argument to any finite time via a new iteration scheme and Strichartz bounds first raised by Klainerman and Machedon in this context.We establish strong and quantitative microscopic to macroscopic convergence of mass and momentum densities up to the 1st blow up time of the limiting Euler equation.We justify that the macroscopic pressure emerges from the space-time averages of micro-scopic interactions via the Strichartz-type bounds.We have hence found a physical meaning for Strichartz-type bounds. 展开更多
关键词 Compressible Euler equation BBGKY hierarchy Quantum many-body dynamics Klainerman-Machedon bounds Modulated energy
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Optimal scheduling of zero-carbon park considering variational characteristics of hydrogen energy storage systems
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作者 Jun Yin Heping Jia +3 位作者 Laijun Chen Dunnan Liu Shengwei Mei Sheng Wang 《Global Energy Interconnection》 EI CSCD 2024年第5期603-615,共13页
Zero-carbon parks have broad prospects in carbon neutralization.As an energy hub,hydrogen energy storage plays an important role in zero-carbon parks.However,the nonlinear characteristics of hydrogen energy storage sy... Zero-carbon parks have broad prospects in carbon neutralization.As an energy hub,hydrogen energy storage plays an important role in zero-carbon parks.However,the nonlinear characteristics of hydrogen energy storage systems(HESSs)have a significant impact on the system economy.Therefore,considering the variable working condition characteristics of HESSs,a hybrid operation method is proposed for HESS,to support the efficient and economic operation of zero-carbon parks,By analyzing the operating principle of a zero-carbon park with HESS,the system structure framework and variable condition linearization model of the equipment in HESS are established.Moreover,considering the energy output characteristics of hydrogen energy storage equipment under variable working conditions,a multimodule hybrid operation strategy is proposed for electrolytic and fuel cells,effectively meeting the thermoelectric load demand of zero-carbon parks in different scenarios.Finally,the economy of the proposed hybrid operation strategy was verified in typical scenarios,using a zero-carbon park embedded with a HESS. 展开更多
关键词 Zero-carbon park variational characteristics Hydrogen energy storage Hybrid operation
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Spatiotemporal variations,influencing factors,and configurational promotion paths of energy efficiency in China’s cities
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作者 Ruyu Xu Keliang Wang +1 位作者 Zhuang Miao Lingxuan Sun 《Chinese Journal of Population,Resources and Environment》 2024年第1期74-86,共13页
The promotion of energy efficiency(EE)helps address energy constraints and promote environmental sustainability.This study comprehensively explores the spatiotemporal variations,influencing factors,and configuration p... The promotion of energy efficiency(EE)helps address energy constraints and promote environmental sustainability.This study comprehensively explores the spatiotemporal variations,influencing factors,and configuration promotion paths of EE in 284 Chinese cities during 2003‒2019 using the global super-efficiency minimum distance to strong efficient frontier(G-S-MinDS),exploratory spatial data analysis(ESDA),multiscale geographically weighted regression(MGWR),and fuzzy set qualitative comparative analysis(fsQCA)methods.The findings are:①China’s cities have an annual average EE of 0.658 with a growth rate of 0.53%,showing considerable promotion potential.②Industrial structure optimization,population agglomeration,economic development,and increased green coverage contribute positively,while government intervention and openness hinder China’s urban EE.③Four configurational promotion paths for enhancing China’s urban EE are identified,where among those paths population density is a core condition,while government intervention is not.This study provides valuable insights into substantially improving urban EE,emphasizing the need for targeted policies to address energy and environmental crises in China. 展开更多
关键词 energy efficiency Spatiotemporal variations Influencing factors Configurational promotion paths
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Spatiotemporal variations of parameters of internal solitary waves in the northern South China Sea
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作者 Yu’ang LIU Yifei JIANG +3 位作者 Xiaojiang ZHANG Zhiyuan WANG Yu CAO Huizan WANG 《Journal of Oceanology and Limnology》 SCIE CAS CSCD 2024年第2期421-438,共18页
The dynamic parameters for internal solitary waves(ISWs)derived from the extended Korteweg-de Vries(eKdV)equation play an important role in the understanding and prediction of ISWs.The spatiotemporal variations of the... The dynamic parameters for internal solitary waves(ISWs)derived from the extended Korteweg-de Vries(eKdV)equation play an important role in the understanding and prediction of ISWs.The spatiotemporal variations of the dynamic parameters of the ISWs in the northern South China Sea(SCS)were studied based on the reanalysis of long-term temperature and salinity datasets.The results for spectrum analysis show that there are definite geographical differences for the periodic variation of the parameters:in shallow water,all parameters vary with a wave period of one year,while in deep water wave components of the parameters at other frequencies exist.Using wavelet analysis,the wavelet power spectral densities in deep water exhibited an inter-annual variation pattern.For example,the wave component of the dispersion coefficient with a wave period of about half a year reached its power peak once every two years.Based on previous work,this inter-annual variation pattern was deduced to be caused by dynamic processes.In further work on the regulatory mechanisms,empirical orthogonal function(EOF)decomposition was performed.It was found that the modes of the dispersion coefficient have different geographical distributions,explaining the reason why the wave components in different frequencies appeared in different locations.The numerical simulation results confirm that the variations in the parameters of the ISWs derived from the eKdV equation could affect the waveforms significantly because of changes in the polarity of the ISWs.Therefore,the periodic variations of the dynamic parameters are related to the geographical location because of dynamic processes operating. 展开更多
关键词 internal solitary waves(ISWs) dynamic parameters eKdV equation spatiotemporal variation polarity empirical orthogonal function(Eof)decomposition
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The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms
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作者 WANG Ji-nan SUN Da-wei 《Chinese Quarterly Journal of Mathematics》 2024年第3期315-323,共9页
We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min... We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough. 展开更多
关键词 Kirchhoff-type equation the existence Positive solution variational method
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Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media
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作者 Maohui Lyu Vrushali A.Bokil +1 位作者 Yingda Cheng Fengyan Li 《Communications on Applied Mathematics and Computation》 EI 2024年第1期30-63,共34页
In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic ... In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations. 展开更多
关键词 Maxwell’s equations Kerr and Raman Discontinuous Galerkin method energy stability
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Three-year Variations of Water, Energy and CO_2 Fluxes of Cropland and Degraded Grassland Surfaces in a Semi-arid Area of Northeastern China 被引量:16
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作者 刘辉志 涂钢 +1 位作者 符淙斌 石立庆 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2008年第6期1009-1020,共12页
Based on 3 years (2003-05) of the eddy covariance (EC) observations on degraded grassland and cropland surfaces in a semi-arid area of Tongyu (44°25′N, 122°52′E, 184 m a.s.1.), Northeast China, seaso... Based on 3 years (2003-05) of the eddy covariance (EC) observations on degraded grassland and cropland surfaces in a semi-arid area of Tongyu (44°25′N, 122°52′E, 184 m a.s.1.), Northeast China, seasonal and annual variations of water, energy and CO2 fluxes have been investigated. The soil moisture in the thin soil layer (at 0.05, 0.10 and 0.20 m) clearly indicates the pronounced annual wet-dry cycle; the annual cycle is divided into the wet (growing season) and dry seasons (non-growing season). During the growing season (from May to September), the sensible and latent heat fluxes showed a linear dependence on the global solar radiation. However, in the non-growing season, the latent heat flux was always less than 50 W m^-2, while the available energy was dissipated as sensible, rather than latent heat flux. During the growing season in 2003-05, the daily average sensible and latent heat fluxes were larger on the cropland surface than on the degraded grassland surface. The cropland ecosystem absorbed more CO2 than the degraded grassland ecosystem in the growing season in 2003-05. The total evapotranspiration on the cropland was more than the total precipitation, while the total evapotranspiration on the degraded grassland was almost the same as the total annual precipitation in the growing season. The soil moisture had a good correlation with the rainfall in the growing season. Precipitation in the growing season is an important factor on the water and carbon budget in the semi-arid area. 展开更多
关键词 WATER energy and flux semi-arid area eddy covariance seasonal and annual variation
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Seasonal variations in the energy budget of Elliot's pheasant (Syrmaticus ellioti) in cage 被引量:6
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作者 Ying LUO Tai-Lin YU +3 位作者 Cheng-Ming HUANG Tong ZHAO Han-Hua LI Chang-Jian LI 《Zoological Research》 CAS CSCD 北大核心 2013年第1期I0024-I0030,共7页
This study aimed to discuss the energy budget of Elliot's pheasant Syrmaticus ellioti in different seasons, with life and health, good growth and normal digestion of Elliot's pheasant as the tested objects, Th... This study aimed to discuss the energy budget of Elliot's pheasant Syrmaticus ellioti in different seasons, with life and health, good growth and normal digestion of Elliot's pheasant as the tested objects, The energy budget of Elliot's pheasant was measured by daily collection of the trial pheasants' excrement in the biological garden of Guangxi Normal University from March 2011 to February 2012. The results showed that the gross energy consumption, metabolic energy and excrement energy varied by season, increasing as temperature decreased. There was significant difference in gross energy consumption, metabolic energy, excrement energy between adults and nonages. There was also a trend that food digestibility of pheasants increases as temperature increases. In the same season, the food digestibility of adults was better than that of nonages. Throughout spring, summer, autumn and winter, the metabolic energy of 4-year adults were 305.77±13.40 kJ/d, 263.67±11.89 kJ/d, 357.23±25.49 kJ/d and 403.12±24.91 kJ/d, respectively, and the nonages were 284.86±17.22 kJ/d, 284. 66±15.16 kJ/d, 402. 26±31.46 kJ/d and 420. 30±31.98 kJ/d, respectively. The minimum metabolic energies were 247.65±21.81 g, 265.86±26.53 g, respectively for each group, detected between 4-year adults and 1-year nonages. Further study is needed to determine whether 29.6 C is the optimal temperature for the Elliot's pheasant. 展开更多
关键词 Elliot's pheasants energy budget Seasonal variations
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The spatiotemporal variation of the wind-induced near-inertial energy flux in the mixed layer of the South China Sea 被引量:2
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作者 LI Juan LIU Junliang +1 位作者 CAI Shuqun PAN Jiayi 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2015年第1期66-72,共7页
On the basis of the QSCAT/NCEP blended wind data and simple ocean data assimilation (SODA), the wind-induced near-inertial energy flux (NIEF) in the mixed layer of the South China Sea (SCS) is estimated by a sla... On the basis of the QSCAT/NCEP blended wind data and simple ocean data assimilation (SODA), the wind-induced near-inertial energy flux (NIEF) in the mixed layer of the South China Sea (SCS) is estimated by a slab model, and the model results are verified by observational data near the Xisha Islands in the SCS. Then, the spatial and temporal variations of the NIEF in the SCS are analyzed. It is found that, the monthly mean NIEF exhibits obvious spatial and temporal variabilities, i.e., it is large west of Luzon Island all the year, east of the Indo-China Peninsula all the year except in spring, and in the northern SCS from May to Septem- ber. The large monthly mean NIEF in the first two zones may be affected by the large local wind stress curl whilst that in the last zone is probably due to the shallow mixed layer depth. Moreover, the monthly mean NIEF is relatively large in summer and autumn due to the passage of typhoons. The spatial mean NIEF in the mixed layer of the SCS is estimated to be about 1.25 mW/m2 and the total wind energy input from wind is approximately 4.4 GW. Furthermore, the interannual variability of the spatial monthly mean NIEF and the Nifio3.4 index are negatively correlated. 展开更多
关键词 near-inertial energy flux mixed layer spatiotemporal variation slab model South China Sea
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The quantum Kirchhoff equation and quantum current and energy spectrum of a homogeneous mesoscopic dissipation transmission line 被引量:2
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作者 崔元顺 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第10期3093-3096,共4页
On the basis of quantization of charge, the loop equations of quantum circuits are investigated by using the Helsenberg motion equation for a mesoscopic dissipation transmission line. On the supposition that the syste... On the basis of quantization of charge, the loop equations of quantum circuits are investigated by using the Helsenberg motion equation for a mesoscopic dissipation transmission line. On the supposition that the system has a symmetry under translation in charge space, the quantum current and the quantum energy spectrum in the mesoscopic transmission llne are given by solving their eigenvalue equations. Results show that the quantum current and the quantum energy spectrum are not only related to the parameters of the transmission llne, but also dependent on the quantized character of the charge obviously. 展开更多
关键词 mesoscopic dissipation transmission line quantum Kirchhoff's equation quantum current quantum energy spectrum
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FINITE TIME BLOW UP OF THE SOLUTIONS TO BOUSSINESQ EQUATION WITH LINEAR RESTORING FORCE AND ARBITRARY POSITIVE ENERGY 被引量:2
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作者 nikolay kutev natalia kolkovska milena dimova 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期881-890,共10页
Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are ... Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals. 展开更多
关键词 Boussinesq equation with linear restoring force finite time blow up arbitrary high positive energy combined power nonlinearities sign preserving functionals
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BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY 被引量:1
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作者 吴秀兰 高文杰 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期1024-1030,共7页
This paper deals with a class of porous medium equation ut=△u^m+f(u)with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on... This paper deals with a class of porous medium equation ut=△u^m+f(u)with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f(u). 展开更多
关键词 porous medium equation BLOW-UP positive initial energy
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Variational Approach for the Adapted Solution of Backw ard Stochastic Differential Equations with Locally Lipschitz Diffusion Coefficients 被引量:1
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作者 谢臻赟 刘奕 《Journal of Donghua University(English Edition)》 EI CAS 2012年第4期341-350,共10页
One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, ... One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise". 展开更多
关键词 backward stochastic differential equation (BSDE) variational approach locally Lipschitz condition EXISTENCE Fointegrable equivalent class UNIQUENESS Brownian bridge
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The Influences of Energy Price Variation on the Prices of Other Industries: A Study Based on Input-Output Price Model 被引量:2
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作者 Aiwen Zhao Ruilin Li 《Open Journal of Energy Efficiency》 2019年第2期35-51,共17页
Energy has laid material foundation for human society during its development. Meanwhile, any change of price in the energy industry may influence social production and people’s life at all levels via an input-output ... Energy has laid material foundation for human society during its development. Meanwhile, any change of price in the energy industry may influence social production and people’s life at all levels via an input-output mechanism under which the change related to energy is surely transmitted to other industries. The price change thus incurred in all industries may adversely affect the realization of macroeconomic objective-maintaining prices at a stable level. It is, therefore, needed to conduct an empirical research related to the impact of price change in energy industry on that in other industries. According to the data coming from “China’s 2015 Input-Output Extension Table (42 Departments)” and four hypothetical basis, this article focuses on four energy sectors and analyzes how deeply the price change of them, by use of input-output model, affects that of other industrial products under five conditions where each of their price rises by 10% individually or simultaneously, and why such an influence occurs. The results show that the price rising of the energies in question leads to an upward growth in the prices of other industrial products, especially when their prices go up simultaneously. Besides, the price increase in the four energy sectors doesn’t influence other industries in an accumulation form but actually leads to a rollback in some of other industries. It is recommended to adopt diversified pricing strategies for different energy products, thus maximizing the value of each specific energy, and meanwhile achieving the goals of energy consumption reduction and price equilibrium. 展开更多
关键词 energy PRICE variation INPUT-OUTPUT PRICE Model
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Emergence of Friedmann Equation of Cosmology of a Flat Universe from the Time-Energy Uncertainty Principle 被引量:1
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作者 Vernon Cooray Gerald Cooray Farhad Rachidi 《Journal of Modern Physics》 2017年第12期1979-1987,共9页
Friedmann equation of cosmology is based on the field equations of general relativity. Its derivation is straight-forward once the Einstein’s field equations are given and the derivation is independent of quantum mec... Friedmann equation of cosmology is based on the field equations of general relativity. Its derivation is straight-forward once the Einstein’s field equations are given and the derivation is independent of quantum mechanics. In this paper, it is shown that the Friedmann equation pertinent to a homogeneous, isotropic and flat universe can also be obtained as a consequence of the energy balance in the expanding universe between the positive energy associated with vacuum and matter, and the negative gravitational energy. The results obtained here is a clear consequence of the fact that the surface area of the Hubble sphere is proportional to the total amount of information contained within it. 展开更多
关键词 Friedmann equation Expansion of the UNIVERSE Vacuum energy Dark energy Time-energy Uncertainty PRINCIPLE Holographic PRINCIPLE HUBBLE Sphere
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ON THE ENERGY EQUATION FOR A SPATIALLY DEVELOPING INSTABILITY WAVE IN THE THEORY OF HYDRODYNAMIC STABILITY
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作者 Zhou Heng (Tianjin University) 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1990年第4期303-304,共2页
In this article,it is shown that the energy equation for a spatially developing disturbance used in all the literatures dealing with the problem of hydrodynamic stability suffers from a small,but crucial error.
关键词 hydrodynamic stability energy equation spatial mode
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EXISTENCE OF INFINITE ENERGY SOLUTION TO THE INELASTIC BOLTZMANN EQUATION WITH EXTERNAL FORCE
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作者 魏金波 张显文 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2131-2140,共10页
In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More precisely, under the assumptions on the bicharacteristic ... In this paper, the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy. More precisely, under the assumptions on the bicharacteristic generated by external force, we prove the global existence of solution for small initial data compared to the local Maxwellian exp(-p|x - v|^2), which has infinite mass and energy. 展开更多
关键词 inelastic Boltzmann equation infinite energy external force
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Application of He’s Variational Iteration Method for the Analytical Solution of Space Fractional Diffusion Equation
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作者 Mehdi Safari 《Applied Mathematics》 2011年第9期1091-1095,共5页
Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of... Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by variational iteration method (VIM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity. 展开更多
关键词 He’s variationAL ITERATION Method FRACTIONAL DERIVATIVE FRACTIONAL Diffusion equation
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Application of He’s Variational Iteration Method and Adomian Decomposition Method to Solution for the Fifth Order Caudrey-Dodd-Gibbon (CDG) Equation
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作者 Mehdi Safari 《Applied Mathematics》 2011年第8期953-958,共6页
In this work we use the He’s variational iteration method and Adomian decomposition method to solution N-soliton solutions for the fifth order Caudrey-Dodd-Gibbon (CDG) Equation.
关键词 variation Iteration Method Adomian Decomposition Method Caudrey-Dodd-Gibbon (CDG) equation
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SOLUTIONS OF GINZBURG-LANDAU EQUATIONS WITH WEIGHT AND MINIMIZERS OF THE RENORMALIZED ENERGY
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作者 Kou Yanlei Ding Shijin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第1期48-60,共13页
In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vort... In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vortices tend to these d points. This provides the connections between solutions of a class of Ginzburg-Landau equations with weight and minimizers of the renormalized energy. 展开更多
关键词 Ginzburg-Landau equation renormalized energy.
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