共查询到20条相似文献,搜索用时 15 毫秒
1.
Miao Changxing 《数学学报(英文版)》1997,13(2):247-268
We consider the scattering problem for the Hartree equation with potential |x|−1 in a space of dimensionn≥2. We prove the existence ofH
m
-modified wave operator for Hartree equation on a dense set of a neighborhood of zero inH
m
(ℝ
n
), meanwhile, we obtain also the global existence for the Cauchy problem of Hartree equation in a space of dimensionn≥2.
This project is supported by the National Natural Science Foundation of China, 19601005 相似文献
2.
Bao Quan YUAN 《数学学报(英文版)》2008,24(2):253-266
The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^*,γ(R^n), with 1〈p〈∞and A = n-(2α-1)p, and for a small external force in a time-weighted weak Morrey space. 相似文献
3.
Consider the Poisson's equation ψ" (x) = -ev-ψ eψ-v-N(x) with the Dirichlet boundary data, and we mainly investigate the inverse problem of determining the unknown function N(x) from a parameter function family. Some uniqueness and stability results in the inverse problem are obtained. 相似文献
4.
LI Song & ZHOU Xinlong Department of Mathematics Zhejiang University Hangzhou China Instititute of Mathematics University of Duisburg-Essen D- Duisburg Germany 《中国科学A辑(英文版)》2006,49(4):439-450
This paper is concerned with multivariate refinement equations of the type where (?) is the unknown function defined on the s-dimensional Euclidean space Rs, a is a finitely supported nonnegative sequence on Zs, and M is an s×s dilation matrix with m := |detM|. We characterize the existence of L2-solution of refinement equation in terms of spectral radius of a certain finite matrix or transition operator associated with refinement mask a and dilation matrix M. For s = 1 and M = 2, the sufficient and necessary conditions are obtained to characterize the existence of continuous solution of this refinement equation. 相似文献
5.
Chmielinski has proved in the paper [4] the superstability of the generalized orthogonality equation |〈f(x), f(y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmielinski by proving a theorem: LetD
n be a suitable subset of ℝn. If a function f:D
n → ℝn satisfies the inequality ∥〈f(x), f(y)〉| |〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ D
n, thenf satisfies the generalized orthogonality equation for anyx, y ∈ D
n. 相似文献
6.
In this note, we prove that there exists a unique global regular solution for multidimensional Landau-Lifshitz equation if
the gradient of solutions can be bounded in space L
2(0, T; L
∞). Moreover, for the two-dimensional radial symmetric Landau-Lifshitz equation with Neumann boundary condition in the exterior
domain, this hypothesis in space L
2(0, T; L
∞) can be cancelled. 相似文献
7.
Jian-hui Long Xi-yan Hu Lei Zhang 《Bulletin of the Brazilian Mathematical Society》2008,39(3):371-386
In this paper, we study the matrix equation X + A*X
−1
A + B*X
−1
B = I, where A, B are square matrices, and obtain some conditions for the existence of the positive definite solution of this equation. Two
iterative algorithms to find the positive definite solution are given. Some numerical results are reported to illustrate the
effectiveness of the algorithms.
This research supported by the National Natural Science Foundation of China 10571047 and Doctorate Foundation of the Ministry
of Education of China 20060532014. 相似文献
8.
Zhi-fei ZHANG School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2007,50(4):485-494
We study the initial value problem for the 2D critical dissipative quasi-geostrophic equation. We prove the global existence for small data in the scale invariant Besov spaces Bp,12/p,1≤p≤∞. In particular, for p=∞, our result does not impose any regularity on the initial data. Our proofs are based on an exponential decay estimate of the semigroup e-tk(-Δ)αand the use of space-time Besov spaces. 相似文献
9.
Liqun Tao 《The Ramanujan Journal》2009,19(3):325-338
In this paper we consider the Diophantine equation x
2+5
m
=y
n
, n>2, m>0. We prove that the equation has no positive integer solutions when 2∤
m, nor when 2∣m under the additional condition (x,y)=1, with the help of Bilu, Hanrot, and Voutier’s deep result in (J. Reine Angew. Math. 539:75–122, 2001).
Supported by the 973 Grant of P.R.C and SRFDP 20040284018. 相似文献
10.
Xin Li 《Advances in Computational Mathematics》2009,30(3):201-230
For a Helmholtz equation Δu(x) + κ
2
u(x) = f(x) in a region of R
s
, s ≥ 2, where Δ is the Laplace operator and κ = a + ib is a complex number with b ≥ 0, a particular solution is given by a potential integral. In this paper the potential integral is approximated by using
radial bases with the order of approximation derived.
相似文献
11.
Abstract. It is proved that the semilinear elliptic problem with zero boundary value 相似文献
12.
§ 1 IntroductionIn this paper we shall study the formation of spatially periodic patterns in extendedsystems described by Swift- Hohenberg equationut=ku - 1 +2x22 u - u3 ,k∈ R. (1.1)This equation was first proposed in 1976 by Swiftand Hohenberg[12 ] as a simple model forthe Rayleigh- B nard instability of roll waves.However,since then an effective m odel e-quation has been proved for a variety of system s in physics and mechanics.The Swift- Hohenberg equation has been studied a … 相似文献
13.
We obtain exact solutions U(x, y, z, t) of the three-dimensional sine-Gordon equation in a form that Lamb previously proposed
for integrating the two-dimensional sine-Gordon equation. The three-dimensional solutions depend on arbitrary functions F(α)
and ϕ(α,β), whose arguments are some functions α(x, y, z, t) and β(x, y, z, t). The ansatzes must satisfy certain equations. These
are an algebraic system of equations in the case of one ansatz. In the case of two ansatzes, the system of algebraic equations
is supplemented by first-order ordinary differential equations. The resulting solutions U(x, y, z, t) have an important property,
namely, the superposition principle holds for the function tan(U/4). The suggested approach can be used to solve the generalized sine-Gordon equation, which, in contrast to the classical equation,
additionally involves first-order partial derivatives with respect to the variables x, y, z, and t, and also to integrate
the sinh-Gordon equation. This approach admits a natural generalization to the case of integration of the abovementioned types
of equations in a space with any number of dimensions.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 370–377, March, 2009. 相似文献
14.
Marc Chamberland 《The Ramanujan Journal》2008,16(2):169-179
The Pythagorean equation is extended to higher dimensions via circulant matrices. This form allows for the set of solutions
to be expressed in a clean yet non-trivial way. The cubic case, namely the equation x
3+y
3+z
3−3xyz=1, was studied by Ramanujan and displays many interesting properties. The general case highlights the use of circulant matrices
and systems of differential equations. The structure of the solutions also allows parametrized solutions of the Fermat equation
in degrees 3 and 4 to be given in terms of theta functions.
相似文献
15.
LICHANGPIN YANGZHONGHUA 《高校应用数学学报(英文版)》1998,13(3):263-270
This paper deals with the steady state bifurcation of the K-S equation in two spatial dimensions with periodic boundary value condition and of zero mean. With the increase of parameter a, the steady state bifurcation behaviour can be very complicated. For convenience, only the cases a=2 and a=5 witl be discussed. The asymptotic expressions of the steady state solutions bifurcated from the trivial solution near a=2 and a=5 are given. And the stability of thenontriviat sotutions bifurcated from a=2 is studied. Of course, the cases a=n^2 m^2,n,m∈N(a≠2,5) can be similarly discussed by the same method which is used to discussing the cases a=2 and a= 5. 相似文献
16.
The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation. The local existence of its solution in Sobolev space Hs (R) with 1 〈 s ≤ 3/2 is derived. 相似文献
17.
Dagmar Medková 《Czechoslovak Mathematical Journal》2007,57(4):1107-1139
The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on
a general open set G in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential
corresponding to a distribution with finite energy supported on ∂G. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed.
The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503. 相似文献
18.
In this paper,the existence of global attractor for 3-D complex Ginzburg Landau equation is considered.By a decomposition of solution operator,it is shown that the global attractor A_i in H~i(Ω) is actually equal to a global attractor Aj in H~j(Ω)(i≠j,i,j = 1,2,…m). 相似文献
19.
Song LI~ 《中国科学A辑(英文版)》2007,50(7):1015-1025
Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form (?)(x)=(?)a(α)(?)(Mx-α),x∈R~s, where the vector of functions(?)=((?)_1,...,(?)_r)~T is in(L_2(R~s))~r,a=:(a(α))_(α∈Z~s)is a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that lim_(n→∞)M~(-n)=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results. 相似文献
20.
D. P. Novikov 《Theoretical and Mathematical Physics》2006,146(3):295-303
We show that under the Euler integral transformation with the kernel (x−z)−α, some solutions of the Fuchs equations (the original pair for the Painlevé VI equation) pass into solutions of a system of
the same form with the parameters changed according to the Okamoto transformation.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 355–364, March, 2006. 相似文献