一类带有阻尼项和源项的波动方程的整体解的存在性(英文)

研究带有阻尼项的非线性波动方程(1.1),得出在初值满足一定条件时,方程的整体解存在,且解的能量是指数衰减的.     

具记忆和变时滞项的二阶发展方程能量衰减率的凸性估计

研究了如下一类具有记忆和变时滞项的抽象发展方程u_(tt)(t)+Au(t)-(∫_0~t g(t-s)Au(s)ds+μ_1h_1(u_t(t))+μ_2h_2(u_t(x,t-T(t)))=▽F(u(t)).通过构造合适的能量泛函和Lyapunov泛函,利用凸函数的一些性质,得到了依赖于h_1及记忆核g的能量衰减估计.此衰减估计可以应用于一些具体的模型.     

带有Gilbert阻尼项的Landau-Lifshitz铁磁链方程解的最佳衰减率

主要研究带有Gilbert阻尼项的Landau-Lifshitz铁磁链方程的柯西问题.当初值的一阶导数适当小时,基于加权能量估计,证明了强解的整体存在性并且给出了解的最优的L2和L∞衰减估计.     

含奇异势和记忆项的四阶抛物方程解的整体存在性与爆破

本文研究一类具有奇异势和记忆项的四阶抛物方程在有界域上的初边值问题.当初值在稳定集中,初始能量在正有界范围内,根据Faedo-Galerkin方法结合Hardy-Sobolev不等式得到了问题解的整体存在性并建立了能量泛函的衰减估计;当初始能量为负时,利用凸方法证明了问题的解在有限时刻爆破并估计了爆破时间上界,该上界依赖于初始能量;当初值位于不稳定集,初始能量有上界时,通过构造辅助泛函获得了一个与初始能量无关的爆破时间上界.     

具有局部非线性反馈的非均质Timoshenko梁的能量衰减估计

该文考虑具有局部非线性反馈的非均质Timoshenko梁的能量衰减估计.由非线性算子半群理论得到系统的适定性;应用乘子方法,给出了系统的能量衰减估计.     

一类具有Taylor阻尼的Klein-Gordon方程解的稳定性分析

研究了一类具有Taylor阻尼的Klein-Gordon方程解的稳定性.通过对松弛函数及初始值进行适当的限制,首先基于位势井理论,得到了整体解的存在性,然后构造新的能量函数,利用凸函数的性质及扰动能量方法,得到了显式的能量衰减估计.研究过程中弱化了对松弛函数的限制,同时得到了更广泛的能量衰减速率估计.     

高频超声中带退化记忆项的MGT方程解的衰减估计北大核心CSCD

研究了高频超声应用中带无穷退化记忆项的Moore-Gibson-Thompson方程τu_(ttt)+α(x)u_(tt)-c^(2)Δu-bΔu_(t)+∫^(∞)_(0)g(s)div[a(x)▽u(t-s)]ds=0解的适定性和衰减速率,其中非负函数a(x)和α(x)是可退化的并满足a(x)+α(x)≥δ>0.该系统是由黏性热松弛流体中波传播模型的线性化而得到的.通过使用Faedo-Galerkin逼近和能量估计,证明了解的适定性.在适当的假设下,通过构造适当的李雅普诺夫泛函,建立了能量的指数或一般衰减结果.     

具变指数源项和强阻尼项的波动方程解的渐近稳定性

该文主要讨论下列具强阻尼项的波动方程的初边值问题u_(tt)-div(|▽u|~(p(x)-2)▽u)-△u_t=|u|~(q(x)-2)u解的渐近行为.通过构造一个新的控制函数和利用Sobolev嵌入不等式,建立了源项和能量泛函之间的定性关系.进而,利用Komornik不等式和能量估计,给出了衰减估计.最后,证明u(x,t)=0是渐近稳定的.     

非线性梁方程初边值问题的能量衰减估计

本文讨论了具阻尼和外力项的非线性梁方程初边值问题的能量衰减估计和外力项的关系,运用一个新的比较不等式,得到了能量和外力项有相同的衰减指数.     

一类具对数源项波动方程的初边值问题

该文考虑一类具对数源项波动方程的初边值问题.利用Galerkin方法结合对数Sobolev不等式和对数Gronwall不等式,对所有初始值得到了整体解的存在性.通过引入位势井,给出了解在时间无穷远处爆破(即指数增长)的充分条件.当具有对数源项的波动方程还带有线性阻尼时,通过构造适当的Lyapunov函数,得到了能量的衰减估计.     

The Laplacian incidence energy of graphs

The Laplacian incidence energy of a graph is defined as the sum of the singular values of its normalized oriented incidence matrix. In this paper, we give sharp upper and lower bounds as well as the Coulson integral formula for the Laplacian incidence energy. Moreover, we show a close relation of the Laplacian incidence energy, normalized incidence energy and Randi? energy.     

再生能源的可持续发展模型

从可持续发展的角度 ,分析了可再生能源的经济学特性 .采用动态经济学的最优控制技术 ,建立了可再生能源的不考虑生产成本及考虑生产成本可持续发展模型 .讨论了效用贴现率、能源生产成本、能源自然增长率对均衡状态能源存量、能源价格、能源消费量的影响 .     

Domain branching in uniaxial ferromagnets: asymptotic behavior of the energy

In this article we analyze the ground state energy of a ferromagnetic bulk sample with strong uniaxial anisotropy in a regime featuring domain branching. We derive the convergence of the micromagnetic energy towards a sharp interface energy in the spirit of Γ-limits. Then we use this convergence to rigorously justify the notion of a minimal energy per cross-section area. Compared to known results, the scaling bounds for the minimal energy are improved to an asymptotic equality.     

Trajectory tracking control of variable length pendulum by partial energy shaping

This paper concerns a trajectory tracking control problem for a pendulum with variable length, which is an underactuated mechanical system of two degrees-of-freedom with a single input of adjusting the length of the pendulum. We aim to study whether it is possible to design a time-invariant control law to pump appropriate energy into the variable length pendulum for achieving a desired swing motion (trajectory) with given desired energy and length of the pendulum. First, we show that it is difficult to avoid singular points in the controller designed by using the conventional energy-based control approach in which the total mechanical energy of the pendulum is controlled. Second, we present a tracking controller free of singular points by using only the kinetic energy of rotation and the potential energy of the pendulum and not using the kinetic energy of the motion along the rod. Third, we analyze globally the motion of the pendulum and clarify the stability issue of two closed-loop equilibrium points; and we also provide some conditions on control parameters for achieving the tracking objective. Finally, we show numerical simulation results to validate the presented theoretical results.     

Copolymer–homopolymer blends: global energy minimisation and global energy bounds

We study a variational model for a diblock copolymer–homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta–Kawasaki energy. In one dimension, on the real line and on the torus, we prove existence of minimisers of this functional and we describe in complete detail the structure and energy of stationary points. Furthermore we characterise the conditions under which the minimisers may be non-unique. In higher dimensions we construct lower and upper bounds on the energy of minimisers, and explicitly compute the energy of spherically symmetric configurations.     

组合模型在我国能源需求预测中的应用

文章首先比较了不同的能源需求预测方法的特点,并选择确定性加随机性时间序列组合模型对我国能源需求进行预测,然后详细介绍了建模的过程,并对模型预测精度和参数稳定性作了评价,结果表明本文采用的组合模型是一种比较有效的预测方法,最后用该模型对我国2004~2020能源需求进行了预测。     

The stability of domain and the pinching of energy about harmonic maps

In this paper, we establish a sharp inequality of the gradient of energy density. We use it in studying stability of domain and pinching of energy. And we get the sharp conclusion respectly. In addition, we connect the existence of non-constant totally geodesic maps with the construction of manifolds on topology and geometry.     

Dynamics of discrete screw dislocations via discrete gradient flow

We present variational approaches (developed in [3,4,11]) to the study of statics and dynamics of screw dislocations in crystals. We model the crystal as a cubic lattice and we give the asymptotic Γ-convergence expansion of the elastic energy induced by a finite family of screw dislocations as the lattice spacing goes to zero. We show that the effective energy associated to the presence of a finite system of screw dislocations coincides with the renormalized energy, studied within the Ginzburg-Landau framework and ruling the interactions between the dislocations. As a byproduct of this analysis, we show the existence of many metastable configurations of dislocations pinned by energy barries. Using the minimizing movement approach á la De Giorgi, we introduce a discrete-in-time variational dynamics, referred to as Discrete Gradient Flow, which allows to overcome these energy barriers. More precisely, we show that lettting first the lattice spacing and then the time step of minimizing movements tend to zero, dislocations move accordingly with the gradient flow of the renormalized energy. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Frequency and dependence of long range temporal correlations in human hippocampal energy fluctuations

Spontaneous energy fluctuations in human hippocampal EEG show prominent amplitude and temporal variability. Here we show hippocampal energy fluctuations often exhibit long‐range temporal correlations with power‐law scaling. In most cases this scaling behavior persisted on time scales in excess of 10 minutes, the maximum duration we could detect with our recording durations. During these epochs we find that the energy fluctuations exhibit long‐range correlations over a broad frequency range (0.5–100 Hz) with greater persistence of the correlations in the lower frequency bands (0.5–30 Hz) than the higher (30–100 Hz). The correlation in hippocampal energy fluctuations is characterized by a bias for energy fluctuations to be followed by similar magnitude fluctuations over all energy scales, i.e. large fluctuations begets large fluctuations and small begets small. © 2005 Wiley Periodicals, Inc. Complexity 10: 35–45, 2005     

The equations of elastostatics in a Riemannian manifold

To begin with, we identify the equations of elastostatics in a Riemannian manifold, which generalize those of classical elasticity in the three-dimensional Euclidean space. Our approach relies on the principle of least energy, which asserts that the deformation of the elastic body arising in response to given loads minimizes over a specific set of admissible deformations the total energy of the elastic body, defined as the difference between the strain energy and the potential of the loads. Assuming that the strain energy is a function of the metric tensor field induced by the deformation, we first derive the principle of virtual work and the associated nonlinear boundary value problem of nonlinear elasticity from the expression of the total energy of the elastic body. We then show that this boundary value problem possesses a solution if the loads are sufficiently small (in a sense we specify).