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本文研究一维空间中带松弛项的单个守恒律方程解的大时间状态估计.在松弛项满足耗散条件下通过对线性化方程Green函数的逐点估计得到方程解在时间充分大时的衰减估计,并由此反映出“弱”惠更斯原理. 相似文献
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主要研究外力函数f 满足一定条件时,半空间上Boussinesq 方程组当n≥3时弱解的L2衰减。先假设解光滑,给出了光滑解的一致L2衰减估计,再通过构造逼近解,对逼近解序列作一致衰减估计,取极限得到弱解的一致L2衰减估计。 相似文献
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基于对线性化方程格林函数的详细分析,研究了偶数维空间带粘性项的非线性波动方程解的大时间状态.得到了解的最佳衰减估计,与惠更斯原理相符. 相似文献
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研究了一类四阶双曲型方程解的空间衰减估计.首先构造方程解的表达式,其次结合截面线积分和面积积分,并利用微分不等式的方法,推导出该表达式的相关估计,最后得到方程解的空间衰减估计. 相似文献
6.
偶数维线性化一般Navier—Stokes方程组的时态渐近性质 总被引:1,自引:0,他引:1
为了得到偶数维线性化一般Navier-Stokes方程组的逐点估计,作者用特征分解和微局部分析方法,对其格林函数进行逐点估计,最终得到方程解在时间充分大时的衰减估计并由此反映出所谓“弱”惠更斯原理。 相似文献
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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. 相似文献
8.
方道元 《数学年刊A辑(中文版)》1999,(4)
本文研究具弱衰减、小初值初始条件的一维Dirac-Klein-Gordon方程组解的存在时间估计问题,结果表明这类问题解的存在时间几乎比e-4大初值的弱衰减条件使得通常的方法不能使用,在此,通过利用Delort曾用过的方程组特征的曲率性质以及2次微局部椭圆正则性解决了该问题. 相似文献
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本文研究了一类具有非线性耗散项的高阶Kirchhoff型方程的初边值问题.通过构造稳定集讨论了此问题整体解的存在性,应用Nakao的差分不等式建立了解能量的衰减估计.在初始能量为正的条件下,证明了解在有限时间内发生blow-up,并且给出了解的生命区间估计. 相似文献
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研究了一个具有三次非线性项的可积的两分量Camassa-Holm系统Cauchy问题解的持久性.通过用权函数估计的方法证明:如果两分量Camassa-Holm系统的初值以及初值的空间导数都以指数形式衰减,则两分量Camassa-Holm系统的强解也在无穷远处以指数形式衰减,进一步,给出了动量的最优衰减估计. 相似文献
11.
Gerassimos Barbatis 《Arkiv f?r Matematik》2007,45(2):197-219
We obtain integral boundary decay estimates for solutions of fourth-order elliptic equations on a bounded domain with regular
boundary. We apply these estimates to obtain stability bounds for the corresponding eigenvalues under small perturbations
of the boundary. 相似文献
12.
In this paper we study quantitative uniqueness estimates of solutions to general second order elliptic equations with magnetic and electric potentials. We derive lower bounds of decay rate at infinity for any nontrivial solution under some general assumptions. The lower bounds depend on asymptotic behaviors of magnetic and electric potentials. The proof is carried out by the Carleman method and bootstrapping arguments. 相似文献
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We establish temporal decay estimates for weak solutions to the Hall-magnetohydrodynamic equations. With these estimates in hand we obtain algebraic time decay for higher order Sobolev norms of small initial data solutions. 相似文献
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On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows 总被引:1,自引:0,他引:1
This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in R~3.Based on linear L~P-L~q estimates,the auxiliary decay properties of the solutions and generalized Gronwall type arguments,some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology. 相似文献
15.
THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS
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Linghai Zhang 《应用数学年刊》2016,32(4):396-417
Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple together the elementary uniform energy estimates of the global weak solutions and a well known Gronwall''s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980''s to study
the optimal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay estimates with sharp rates of the global weak solutions of the Cauchy problems for $n$-dimensional incompressible Navier-Stokes equations, for the $n$-dimensional magnetohydrodynamics equations
and for many other very interesting nonlinear evolution equations with dissipations can be established. 相似文献
16.
We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2004,56(1):147-155
The author is concerned with the long time asymptotic behaviors of the global weak solutions of some nonlinear evolution equations. First of all, he derives some uniform L1 and L∞ upper bounds for the solutions, under some mild conditions. Then, by applying the well-known Fourier splitting method and the L1 estimates, he asserts the L2 decay estimates of the solutions. The rates of decay are sharp in the sense that the integral of the initial data over is nonzero. 相似文献
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LinghaiZhang 《应用数学学报(英文版)》2004,20(1):59-76
We establish the optimal rates of decay estimates of global solutions of some abstract differentialequations,which include many partial differential equations.We provide a general treatment so that any futureproblem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied.Themain hypotheses are the existence of global solutions of the equations and some growth control of the Fouriertransform of the solutions.We establish the optimal rates of decay of the solutions for initial data in differentspaces.The main ingredients and technical tools are the Fourier splitting method,the iteration skill and theenergy estimates. 相似文献
19.
Hiromichi Hashimoto 《Journal of Differential Equations》2007,237(2):491-525
We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient. 相似文献
20.
De G. Akmel & L. C. Bahi 《偏微分方程(英文版)》2013,26(1):48-75
We study the dynamics of a piecewise (in time) distributed optimal control problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutions for an optimal distributed control problem associated with the Generalized MHD equations is studied. First, a quasi-optimal solution for the Generalized MHD equations is constructed; this quasi-optimal solution possesses the decay (in time) properties. Then, some preliminary estimates for the long-time behavior of all solutions of Generalized MHD equations are derived. Next, the existence of a solution of optimal control problemis proved also optimality system is derived. Finally, the long-time decay properties for the optimal solutions is established. 相似文献