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给定主曲率函数的曲面存在性定理 总被引:3,自引:0,他引:3
黄宣国 《数学年刊A辑(中文版)》1997,(6)
本文给出了R3,R2,1内给定主曲率函数的一类特殊曲面的局部、整体存在性定理的一个充要条件. 相似文献
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1.引言方程是在国内外引起广泛关注的一类重要的非线性发展方程.文[1]在函数f(s)满足局部 Lip-schitz条件及单调性条件(f(s2)-f(s1))(s2-s1)> 0的假设下得到了(1.1)初边值问题整体弱解的存在与唯一性;文[2]用 Galerkin方法,研究了(1.1)的初边值问题,周期边值问题和初值问题,并在函数f’(s)下方有界的假设下得到了整体强解的存在与唯一性. 本文在有限区域 QT=[0,1]×[0,T](T> 0)上讨论方程(1.1)带有初值条件和边值条件(u(x,t)为未知… 相似文献
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具有特殊扩散过程的反应扩散方程 总被引:1,自引:0,他引:1
谭忠 《数学年刊A辑(中文版)》2001,(5)
本文考虑如下具有特殊扩散系数的化学反应扩散方程的整体解存在性、渐近性和局部解有限时间爆破,这里Ω是RN(N≥3)中的光滑有界区域,0∈Ω,1<P<N+2/N-2. 相似文献
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唐宏岩 《数学年刊A辑(中文版)》2001,(4)
本文主要考虑从黎曼曲面到S2的非均匀Landau-Lifshitz方程组的解的存在性.证明了对于适当初始值,方程是存在唯一的,除有限个点外处处正则的整体解,并且该解在每一奇点处爆破成一个光滑的调和映射 还讨论了方程组在IR2上定常解的不存在性. 相似文献
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叶常青 《数学物理学报(A辑)》2001,21(1):138-144
以Schauder Tychonoff不动点定理为工具,建立了一类犚2 上奇异非线性双调和方程正
的径向对称整体解的存在定理,并给出了解的有关性质. 相似文献
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该文讨论二维无界带形区域中Navier-Stokes方程其中Ω=(0,d)×R,d>0为一常数,u与p为未知量,其中u=(u1,u2)为速度场,p表示压力.我们证明了当u0∈H,f∈V且f[log(e+|x|2)]1/2∈L2(Ω)时,问题(I)在H中存在整体吸引子A,它是的一个子集.对A的Hausdorff维数与Fractal维数我们也给出了估计. 相似文献
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本文研究了FDE 整体解的存在性及其零解的全局吸引性,所得结果应用于具有时滞的单种群人口模型 则改进了文[1,2]中的相应结论. 相似文献
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本文以两类非线性抛物型积分微分方程为例,首次尝试将插值后处理思想[1]应用到非线性发展型方程上,获得了半离散和全离散有限元解,经插值后处理之后在L∞(H1);L∞(L2)模意义下,整体超收敛1阶的高精度,并且计算量没有因此而增加.本文引进并证明较文[2]更广泛的一类椭圆H1-Volterra投影的H1;L2,H-1模最优估计.本文的分析方法可在各类发展型微分及积分微分方程上面通用. 相似文献
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V. E. Zakharov A. V. Odesskii M. Cisternino M. Onorato 《Theoretical and Mathematical Physics》2014,180(1):759-764
We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equations with a nonlinearity of the type u?u/?x. Our aim is to find the most general nontrivial form of the dispersion relation ω(k) for which the five-wave interaction scattering matrix is identically zero on the resonance manifold. As could be expected, the matrix in one dimension is zero for the Korteweg-de Vries equation, the Benjamin-Ono equation, and the intermediate long-wave equation. In two dimensions, we find a new equation that satisfies our requirement. 相似文献
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Jong Uhn Kim 《Journal of Differential Equations》2006,228(2):737-768
We discuss the Cauchy problem for the stochastic Benjamin-Ono equation in the function class Hs(R), s>3/2. When there is a zero-order dissipation, we also establish the existence of an invariant measure with support in H2(R). Many authors have discussed the Cauchy problem for the deterministic Benjamin-Ono equation. But our results are new for the stochastic Benjamin-Ono equation. Our goal is to extend known results for the deterministic equation to the stochastic equation. 相似文献
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Nonlinear stability of nonlinear periodic solutions of the regularized Benjamin-Ono equation and the Benjamin-Bona-Mahony equation with respect to perturbations of the same wavelength is analytically studied. These perturbations are shown to be stable. We also develop a global well-posedness theory for the regularized Benjamin-Ono equation in the periodic and in the line setting. In particular, we show that the Cauchy problem (in both periodic and nonperiodic case) cannot be solved by an iteration scheme based on the Duhamel formula for negative Sobolev indices. 相似文献
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In this paper, the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed. Stability of the semi-discrete scheme is proved and error estimate in H1/2-norm is obtained. 相似文献
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In this paper we show that the flow map of the Benjamin-Ono equation on the line is weakly continuous in L 2(?), using “local smoothing” estimates. L 2(?) is believed to be a borderline space for the local well-posedness theory of this equation. In the periodic case, Molinet (Math. Ann. 337, 353–383, 2007) has recently proved that the flow map of the Benjamin-Ono equation is not weakly continuous in $L^{2}(\mathbb{T})In this paper we show that the flow map of the Benjamin-Ono equation on the line is weakly continuous in L
2(ℝ), using “local smoothing” estimates. L
2(ℝ) is believed to be a borderline space for the local well-posedness theory of this equation. In the periodic case, Molinet
(Math. Ann. 337, 353–383, 2007) has recently proved that the flow map of the Benjamin-Ono equation is not weakly continuous in
L2(\mathbbT)L^{2}(\mathbb{T}). Our results are in line with previous work on the cubic nonlinear Schr?dinger equation, where Goubet and Molinet (Nonlinear
Anal. 71, 317–320, 2009) showed weak continuity in L
2(ℝ) and Molinet (Am. J. Math. 130, 635–683, 2008) showed lack of weak continuity in
L2(\mathbbT)L^{2}(\mathbb{T}). 相似文献
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Xueshang Feng & Xiaoyou Han 《偏微分方程(英文版)》1995,8(1):36-42
The decay properties of global solutions for the Benjamin-Ono equation of high order are obtained as |x| → ∞. An Iorio's type result is derived for this equation. 相似文献
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Xavier Carvajal 《Journal of Mathematical Analysis and Applications》2009,351(1):440-455
In this work we obtain results on the estimates of low Sobolev norms for solutions of some nonlinear evolution equations, in particular we apply our method for the complex modified Korteweg-de Vries type equation and Benjamin-Ono equation. 相似文献
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V. I. Zhuk 《Journal of Applied Mathematics and Mechanics》1999,63(6):893-908
Large-scale structures with an inviscid, non-linear subdomain (deck) on the bottom of a boundary layer in the case of subsonic and transonic free stream velocities are considered. A class of locally inviscid perturbations with an internal line of discontinuity of the tangential velocity, which leads to the appearance of a free term on the right-hand side of the Benjamin-Ono equations, is investigated. The shape of the above-mentioned line is sought and it is determined from the solution of a system of one-dimensional non-stationary equations in which, apart from the Benjamin-Ono equation, a kinematic condition and an equation for the inviscid deck close to the wall also occur. An example of a periodic, non-linear solution is constructed and amplitude constraints which ensure its realization are formulated. 相似文献
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The current paper is devoted to the Cauchy problem for the stochastic generalized Benjamin-Ono equation.By establishing the bilinear and trilinear estimates in some Bourgain spaces,we prove that the Cauchy problem for the stochastic generalized Benjamin-Ono equation is locally well-posed for the initial data u_0(x,w)∈L~2(Ω;H~s(R)) which is F_0-measurable with s≥1/2-α/4 and Φ∈L_2~(0,s).In particular,when α=1,we prove that it is globally well-posed for the initial data u_0(x,w)∈L~2(Ω;H~1(R)) which is F_0-measurable and Φ∈L_2~(0,1).The key ingredients that we use in this paper are trilinear estimates,the Ito formula and the Burkholder-Davis-Gundy(BDG) inequality as well as the stopping time technique. 相似文献
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Solitary waves of arbitrary amplitude are found to exist for a class of unbounded stratified flow configurations. In special cases the solutions are similar to those obtained from the Benjamin-Ono equation. 相似文献