共查询到20条相似文献,搜索用时 17 毫秒
1.
Nakao HAYASHI Pavel I. NAUMKIN 《数学学报(英文版)》2006,22(5):1441-1456
We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equation ut+uux-uxx+uxxx=0,x∈R,t〉0. We are interested in the large time asymptotics for the case when the initial data have an arbitrary size. We prove that if the initial data u0 ∈H^s (R)∩L^1 (R), where s 〉 -1/2, then there exists a unique solution u (t, x) ∈C^∞ ((0,∞);H^∞ (R)) to the Cauchy problem for the Korteweg-de Vries-Burgers equation, which has asymptotics u(t)=t^-1/2fM((·)t^-1/2)+0(t^-1/2) as t →∞, where fM is the self-similar solution for the Burgers equation. Moreover if xu0 (x) ∈ L^1 (R), then the asymptotics are true u(t)=t^-1/2fM((·)t^-1/2)+O(t^-1/2-γ) where γ ∈ (0, 1/2). 相似文献
2.
(陈芳跃)OntheSolutionoftheFeigenbaum'sFunctionalEquation¥ChenFahgyue(Dapt.ofMath.,ZhejiangNormalUniv.,Jinhua,Zhejiang,321004)Int... 相似文献
3.
Yingqiu GU 《数学年刊B辑(英文版)》2007,28(5):499-506
In this paper,the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation.This procedure of resolution is based on a canonical form of the metric.According to this procedure,the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution. 相似文献
4.
Robert M. Strain 《偏微分方程通讯》2013,38(10):1551-1586
The Balescu–Lenard equation from plasma physics is widely considered to include a highly accurate correction to Landau's fundamental collision operator. Yet so far it has seen very little mathematical study. We perform an extensive linearized analysis of this equation, which includes determining the asymptotic behavior of the new components of the linearized operator and establishing time decay rates for the linearized equation. 相似文献
5.
We consider the Korteweg-de Vries (KdV) equation in the form ut+uux+uxxx=0(1) which is a nonlinear hyperbolic equation and has smooth solutions for all the time. There are a vast of results can be found in the literature for this equation, both theoretical and numerical. However, several good reasons account for needs of another numerical study of this equation are listed in[1]. Among them, the most convincing one might be that the wave equations have the multi-symplectic structure (cf. [2]), and the KdV equation is therefore a 相似文献
6.
Xu-Qian Fan 《manuscripta mathematica》2006,120(4):435-467
One of the main goals of this paper is to solve the Poincaré–Lelong equation on a class of Kähler manifolds with nonnegative holomorphic bisectional curvature, $\mathrm{Ric}(x)\geq \left(a\ln\ln\left(10+r(x)\right)\right)\Big/\big.\left(\left(1+r^2(x)\right)\ln(10+r(x))\right)One of the main goals of this paper is to solve the Poincaré–Lelong equation on a class of K?hler manifolds with nonnegative holomorphic bisectional curvature, for some a > 67(n + 4)2. We will also study the Poisson equation on complete noncompact manifolds which satisfy volume doubling and Poincaré inequality. 相似文献
7.
In this note, we study the global existence of classical solutions for the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5. Based on the Schauder type estimates and energy estimates, we establish the global existence of classical solutions. 相似文献
8.
Let H, K be two Hilbert spaces over complex field A. Let B(HI, K) denote the set of all bounded linear operators from H to K. If H=K, we write B(H) instead of B(H, K). Consider the operator defined by the equation 相似文献
9.
Consider the system of ordinary differential equation u”(t)+grad G(u(t))=p(t),(1)where p:R→R”is continuous and 2π periodic and G:R~π→R has continuous secondorder partial derivatives.The system can be interpreted physically as the Newto-nian equation of motion of a mechanical system subject to conservative internalforces and the periodic external forces. 相似文献
10.
Let Ω be a convex domain in the (x, y) plane with boundary . Denote by n=(n_x, n_y) the outward unit normal to. Consider the following problem (1) (2) where μ, v are real parameters and σ=σ(x, y) satisfies σ≥σ_0>0. Equation (1) arises in neutron transport theory. In this paper, we study theoretically the stability and convergence properties of a discontinuous Galerkin approximation to prob- 相似文献
11.
OntheApproximateFunctionalEquationofRiemannzeta-FunctionWangWei(王炜)(Dept.ofMath.,ShandongUniversity)Jinan,Shandong250100Commu... 相似文献
12.
Ukrainian Mathematical Journal - For a nonlinear kinetic Boltzmann equation that describes the model of rough spheres, we construct its approximate solution in the form of a continual distribution... 相似文献
13.
§1. In 1972,St.Znam posed the problem whether for every s>1 thereexist integers x_i>1,i=1,…,s such that x_i is a proper divisor of the numberx_1…x_(i-1)x_(i 1)…x_s 1 for i=1,…, s.Without loss of generality, we may assume1相似文献
14.
The extremum problem for the Wiener–Hopf equation obtained by replacing the condition u(x) = 0, x < 0, by the condition of the minimum of the quadratic functional of the function u(x)exp(–x), – < x < , is solved in closed form. 相似文献
15.
G. G. Grahovski A. J. Mohammed H. Susanto 《Theoretical and Mathematical Physics》2018,197(1):1412-1429
Our purpose is to develop the inverse scattering transform for the nonlocal semidiscrete nonlinear Schrödinger equation (called the Ablowitz–Ladik equation) with \(\mathcal{PT}\) symmetry. This includes the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data, and the fundamental analytic solutions. In addition, we study the spectral properties of the associated discrete Lax operator. Based on the formulated (additive) Riemann–Hilbert problem, we derive the one- and two-soliton solutions for the nonlocal Ablowitz–Ladik equation. Finally, we prove the completeness relation for the associated Jost solutions. Based on this, we derive the expansion formula over the complete set of Jost solutions. This allows interpreting the inverse scattering transform as a generalized Fourier transform. 相似文献
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17.
This paper gives a new and direct proof for McKean’s theorem (McKean in Asian J. Math. 2:867–874, 1998) on wave breaking of the Camassa–Holm equation. The blow-up profile is also analyzed. 相似文献
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19.
《数学研究与评论》1987,(2)
An unsolved problem is to enumerate all solutions for the matrix equation A~2=Jwhere A is an n×n (0.1)-matrix and J is the n×n matr trix with every entry being 1. Here we present a family of n×n generalized circulant (0.1)-matrices each of whose square is J. Moreover. the existence of this family is unique up to permutational similarity. 相似文献