共查询到20条相似文献,搜索用时 62 毫秒
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本文在Nanach空间中,针对具广泛意义的满足条件(I)和条件(J)的增生映象,首次给出了二阶发展方程及其相应差分近似方程解的强收敛和弱收敛的充分必要条件;同时,对一般m-增生映象也给出了一个差分方程解弱收敛的充分条件,这里所得结论有助于人们对该类问题的整体认识。 相似文献
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1引言设Ω为R2中有界凸多边形区域,f(x)∈L2(Ω),λ为非负常数,面为LaPlace算子,考虑下面定解问题:我们在空间区域采用有限元剖分,在时间轴上采用[1]提出的一类差分格式,本文证明(1.1)的有限元解当L、co时收敛到下面椭圆方程(1.2)的有限元解:从而可应用[2]提出的具有并行本性的差分格式得到椭圆问题(1.幻的有限元解.2.预备知识设J为o上的拟一致三角剖分,vnCHI(n)为相应于J的线性协调元空间,7T:H‘(m、K为插值算子,使对J的任意节点P,7T。(P)=。(P)·我们用下述格式求解(1.1):求。h+IEVh… 相似文献
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1引言 抛物型方程是一类十分重要的方程,它出现在很多数学物理问题中,对这类方程的研究已有大量工作,如[10-12]等.随着无穷维动力系统研究的深入,人们越来越关心系统的长时间性态,而追踪系统长时间性态很大程度上依赖数值计算. 相似文献
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在考虑强阻尼效应的情形下,建立了一类轴向载荷作用下的波动方程.研究一类具有强阻尼的非线性波动方程的初边值问题的整体解的性态.以Sobolev空间的性质为工具,利用Faedo-Galerkin方法,证明了该方程在线性边界条件下弱解的存在唯一性,为力学中具有阻尼结构的振动问题的研究提供了重要依据. 相似文献
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郑州工程学院数理系 《数学物理学报(A辑)》2004,24(3):329-336
该文考虑一类新的非线性方程(|ut|r-2ut)t-Δutt-Δu-ρ(t)Δut=f(u) 的初边值问题,利用小扰动法证明了整体弱解的
存在性,借用位势井的概念得到了解的稳定性.〖HT5”H〗关键词:〖HT5”SS〗非线性发展方程;初边值问题;整体弱解;稳定性. 相似文献
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讨论具强非线性源和对流项的一般渗流方程以R^N中某一Radon测度为初始迹的Cauchy问题弱解的存在唯一性。 相似文献
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一类修正的Navier-Stokes方程的长时间性态 总被引:3,自引:0,他引:3
该文主要讨论,Rn上一类修正的 Navier-Stokes 方程弱解的长时间性态, 通过进一步改进Fourier分解方法, 得到了当初速度u0∈ L2 ∩L1时其弱解在L2 范数下的最优衰减率为 (1+t)n/4 同时该文也给出了修正的Navier-Stokes 方程与经典Navier-Stokes 方程的误差估计. 相似文献
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DECAYESTIMATIONSOFTHESOLUTIONOFANONLINEARPSEUDOPARABOLICEQUATIONShenLongjun;ZhangLinghai(Inst.ofAppl.Phys.&Comput.Math.,P.O.B... 相似文献
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THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION 总被引:1,自引:0,他引:1
Tang Rongrong 《Annals of Differential Equations》2006,22(4):569-572
In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently. 相似文献
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1 IntroductionIn the heat-conduction equationp is the density,c is the specific heat,k is the thermal conductivityLet u = w -- wco be therelative temperature, where woo is the environmental temperature. In many cases, the thermalconductivity k is dependent of the temperature,forrexample, the heat-conduction of electron iuthe plasma body and the radiation heat-conduction in the high temperature,k(u) = uoum--' (m > 1).Assume that p, c are constants, then the equation (1.1) can be written asWe c… 相似文献
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THE DYNAMICAL BEHAVIOR OF FULLY DISCRETE SPECTRAL METHOD FOR NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED 总被引:2,自引:0,他引:2
向新民 《高等学校计算数学学报(英文版)》1999,(2)
Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0<λ<2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to disscus 相似文献
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Yanni Zeng 《数学物理学报(B辑英文版)》2012,32(1)
We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a h... 相似文献
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1.引言随着无限维动力系统研究的发展和深入,人们对非线性发展方程长时间性态的研究越来越重视[1-6],而这种研究在很大程度上依赖于数值计算的结果,因此,计算结果是否可靠,计算格式先得是否合适都是值得探讨和深入研究的问题17-10.广义KdV-Burg6rs方程是一类重要的非线性发展方程,在实际问题中也有着广泛的应用,因此,对它的研究即有理论价值也有实际意义.本文讨论如下的广义KdV-Burgers方程的周期初值问题其中a,q是已知实常数,且a>0八。),g(。),h00是已知实函数.文[10]对上述问题构造了半离散的Fourier谱逼近… 相似文献
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Tang Rongrong 《Annals of Differential Equations》2005,21(4):587-591
In this paper, using the layer theory, a class of singularly perturbed Robin problem of nonlinear non-autonomous equation is considered. According to the different regions of the boundary value, the asymptotic behaviors of solution for the original problem are obtained simply and conveniently. 相似文献
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Liang Ruixi Peng Jun Shen Jianhua 《Annals of Differential Equations》2006,22(4):502-510
The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures. 相似文献
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In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes). 相似文献
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This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in R~(1+1). It is shown that the solution will tend to travelling wave solution when time tends to infinity. 相似文献