多维的一般的BBM-Burgers方程解的逐点估计

研究R~n中一般的BBM-Burgers方程解的渐进行为.运用Green函数法和Fourier分析方法得到了在非零常状态u~*附近小扰动解的逐点估计,作为一个推论,又得到了L~p(R~n)(1≤p∞)空间解的最佳的衰减估计.     

具有线性阻尼Boussinesq方程解的空间衰减估计

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.     

一维对流扩散方程解的逐点衰减估计

本文研究一维空间对流扩散方程柯西问题.利用格林函数,频谱分解,傅立叶变换等方法,得到了方程解的逐点估计.结果显示解沿特征线作传播.     

高维BBM-Burgers方程解的衰减估计

本文研究了多维空间的Benjamin-Bona-Mahony-Burgers方程.在解整体存在的前提下,利用能量积分、时频分解等方法,得到此方程柯西问题解的衰减估计,并且此方程的衰减速率与热传导方程的相同.     

一类具弱非线性耗散项粘弹性波方程解的能量衰减估计

通过运用扰动能量方法研究了一类具有弱非线性耗散项粘弹性波方程解的能量衰减性,其中耗散项显依赖于时间t,得到解的衰减率依赖于阻尼的增长速度和t的函数.     

具有阻尼的半线性波动方程解的衰减估计

研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|~(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R~n为有界域,当n≥3时,1相似文献   

三维Zakharov-Kuznetsov方程解的衰减性

考虑三维Zakharov-Kuznetsov方程的初值问题,证明了该初值问题解的指数衰减性.这个性质与加权Sobolev空间中解的持久性及该问题解的唯一连续性相关.     

具粘性拟线性波方程的能量衰减估计

给出下列具粘性拟线性波方程初边值问题解的能量衰减估计u_(tt)(t,x)-div{σ(|▽u(t,x)|~2)▽u(t,x)}-△u(t,x)-△ut(t,x)+δ|u_t(t,x)|~(p-1)u_t(t,x)=μ|u(t,x)|~(q-1)u(t,x),x∈Ω,t∈(0,T),u(t,x)|■Ω=0,t∈(0,T),u(0,x)=u_0(x),u_t(0,x)=u_1(x),x∈Ω,其中Ω是R~N(N≥1)中具有光滑边界■Ω的区域,p≥1,q1,δ0,μ0,△表示Laplace算子,▽表示梯度算子和σ(s)是一给定的非线性函数.证明的思想是应用一已知的积分不等式,证明以上初边值问题解的能量衰减估计.     

可压Navier-Stokes方程解的最高阶导的最佳衰减估计

该文研究可压Navier-Stokes方程Cauchy问题光滑解的衰减估计问题.假设初始扰动在Hl(R3)(l≥3)中充分小,且属于H1(R3)(0≤s＜5/2),通过对解的高低频分解,结合谱分析和能量估计方法,得到解各阶导数的最佳衰减估计结果.     

带有对数非线性源的p-Kirchhoff方程解的整体存在性和衰减估计

考虑带有对数非线性源的p-Kirchhoff方程的初边值问题,此问题可用来描述热传播的过程和种群密度的演化.首先利用Galerkin方法,对数Sobolev不等式以及Gronwall不等式,再结合Lions引理,得到其局部解的存在性.同时引入修正泛函研究势井深度,结合势井理论,建立先验估计,得到解的整体存在性和衰减估计,推广和改进了已有结果.     

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.     

ON THE DECAY AND SCATTERING FOR THE KLEIN-GORDON-HARTREE EQUATION WITH RADIAL DATA

In this paper,we study the decay estimate and scattering theory for the Klein-Gordon-Hartree equation with radial data in space dimension d≥3.By means of a compactness strategy and two Morawetz-type estimates which come from the linear and nonlinear parts of the equation,respectively,we obtain the corresponding theory for energy subcritical and critical cases.The exponent range of the decay estimates is extended to 0<γ≤4 and γ相似文献   

DEGENERATE BOUNDARY LAYER SOLUTIONS TO THE GENERALIZED BENJAMIN-BONAMAHONY-BURGERS EQUATION

This paper is concerned with the convergence rates of the global solutions of the generalized Benjamin-Bona-Mahony-Burgers(BBM-Burgers) equation to the corresponding degenerate boundary layer solutions in the half-space.It is shown that the convergence rate is t-(α/4) as t →∞ provided that the initial perturbation lies in H α 1 for α < α(q):= 3 +(2/q),where q is the degeneracy exponent of the flux function.Our analysis is based on the space-time weighted energy method combined with a Hardy type inequality with the best possible constant introduced in [1].     

矩阵方程的最小二乘解

1　引言与引理设 Rm× n表示所有 m× n阶实矩阵的集合 ,ORn× n为所有 n阶实正交矩阵的全体 ,In 是 n阶单位矩阵 .AT、A+、rank A分别表示矩阵 A的转置、MP逆及秩 ;‖·‖是矩阵的Frobenius范数 .此外 ,对于 A =(αij)∈ Rs× s,B =(βij)∈ Rs× s,A * B表示 A与 B的Hadamard积 ,其定义为 :A* B=(αijβij) 1≤ i,j≤ s,现考虑如下问题 :问题 P　给定 A∈Rn× m,B∈Rp× m,D∈Rm× m求 X∈Rn× p,使得Φ =‖ ATXB - BTXTA - D‖ =m in　　我们知道 ,矩阵方程 ATX B- BTXTA=D在自动控制理论中有很重要的作用[1 ,2 ] .…     

GLOBAL CLASSICAL SOLUTIONS OF THE BOLTZMANN EQUATION NEAR MAXWELLIANS

Global classical solutions near Maxwellians are constructed for the Bolt.zma.nn equation in a periodic box with angular soft cutoff, that is, -3<γ< 0. The construction of global solution is based on an energy method used in [9].     

一类四阶非线性波动方程解的爆破与衰减

本文研究了非线性阻尼项与源项的竞争对具有强阻尼项的四阶波动方程解的影响.利用不动点原理和势井方法给出了方程局部弱解存在唯一性满足的条件,证明了当mp且初始能量E(0)0时,解将在有限时间内爆破.同时对m,p的大小关系不加任何限制但存在t_0使0E(t_0)d的情况下,利用稳定集,研究了整体解的存在性,并得到了解的能量衰减估计.最后借助修正的能量泛函,指出当m≥p时弱解也是整体存在的,推广并改进了文献[1-6]中的结果.     

全空间上一类非齐次椭圆方程正解的衰减

本文研究了非齐次椭圆方程不同衰减正解的存在性和衰减问题.利用上下解方法,得到了两个有着不同衰减的正解的存在性,推广了文献[2]中非齐次方程正解的存在性.     

GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

The initial boundary value problem for a viscoelastic equation | u t | ρ u tt △u-△u tt + t 0 g(ts)△u(s)ds + | u t | m u t = | u | p u in a bounded domain is considered, where ρ, m, p > 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature.     

POINTWISE ESTIMATE OF SOLUTIONS OF ISENTROPIC NMIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSIONS

1 IntroductionIn this paPer, we are interested in tlie time-asymptotic behavior of solutions to isentropicNavier-stokes equations in even space-dimensions. Recently many people began to study it'sasymptotic behavier when time is large enough. This can be manifested in tlie after refer-ences. For the pointwise estimate of solution to generaJ hyperbolic-parabolic systems in onespace dimension see Liu and Zeng[']. In several space variables, Kawashima[31 has studiedgeneral hyperbolic-parabolic…