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1.
In this paper, we establish the existence and uniqueness of a BV solution to an initial boundary value problem for a nonlinear integro-differential equation, which is related to a denoising and deblurring variational model in image restoration. Several experiments relevant to the restoration model are performed and numerical results are discussed.  相似文献   

2.
再生核空间W22[0,∞)中一类积分-----微分方程精确   总被引:2,自引:0,他引:2  
李云晖  崔明根 《计算数学》1999,21(2):188-198
In this paper, we discuss the definite solution problem ofintegro-differetial equation, give the exact solution to the definitesolution problem of integro-differential equation in space W22 [0,∞) of reproducing kernel.  相似文献   

3.
In this paper, we formulate a general framework of an analytic approximation of the solutions to some It o stochastic integro-differential equations defined on sub-intervals of an arbitrary part of the time-interval [0,1] and connected at successive division points. The integral parts and coefficients of the equation are approximated by their Taylor polynomial which series up to arbitrary derivatives. The suggested approximations converge to the initial solution in the Lp-th norm with some order.  相似文献   

4.
In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time. By introducing the "blow-up factor K(u,ut)" we get some new results, which generalize the conclusions of [3] and [4].  相似文献   

5.
Nonlinear Schroedinger equation arises in many physical problems. There are many works in which properties of the solution are studied. In this paper we use fully discrete Fourier spectral method to get an approximation solution of nonlinear weakly dissipative Schroedinger equation with quintic term. We give a large-time error estimate and obtain the existence of the approximate attractor A N^k.  相似文献   

6.
This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.  相似文献   

7.
In this paper, we consider generalized BBM equation with nonlinear terms of high order.In the case of p=1/2, p=1 and p=2, the exact periodic solutions to G-BBM equation are obtained by means of proper transformation, which degrades the order of nonlinear terms. And we prove that if p ≠ 1/2,p ≠ 1 or p ≠ 2, G-BBM equation does not exist this kind of periodic solution.  相似文献   

8.
The singularly perturbed boundary value problem of scalar integro-differential equations has been studied extensively by the differential inequality method . However, it does not seem possible to carry this method over to a corresponding nonlinear vector integro-differential equation. Therefore , for n-dimensional vector integro-differential equations the problem has not been solved fully. Here, we study this nonlinear vector problem and obtain some results. The approach in this paper is to transform the appropriate integro-differential equations into a canonical or diagonalized system of two first-order equations.  相似文献   

9.
In this paper, we study a generalized thin film equation which is relevant to capillary driven flows of thin films of power-law fluids. We prove that the generalized thin film equation in dimension d ≥ 2 has a unique C^1 source type radial self-similar nonnegative solution if 0 〈 n 〈 2p - 1 and has no solution of this type if n ≥ 2p - 1.  相似文献   

10.
In this paper, we consider the scattering for the nonlinear Schr¨odinger equation with small,smooth, and localized data. In particular, we prove that the solution of the quadratic nonlinear Schr¨odinger equation with nonlinear term |u|2involving some derivatives in two dimension exists globally and scatters. It is worth to note that there exist blow-up solutions of these equations without derivatives. Moreover, for radial data, we prove that for the equation with p-order nonlinearity with derivatives, the similar results hold for p ≥2d+32d-1and d ≥ 2, which is lower than the Strauss exponents.  相似文献   

11.
Abstract With Littlewood–Paley analysis, Peetre and Triebel classified, systematically, almost all the usual function spaces into two classes of spaces: Besov spaces and Triebel–Lizorkin spaces ; but the structure of dual spaces of is very different from that of Besov spaces or that of Triebel–Lizorkin spaces, and their structure cannot be analysed easily in the Littlewood–Paley analysis. Our main goal is to characterize in tent spaces with wavelets. By the way, some applications are given: (i) Triebel–Lizorkin spaces for p = ∞ defined by Littlewood–Paley analysis cannot serve as the dual spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations among these above spaces and some relations among and L 1 are studied. Supported by NNSF of China (Grant No. 10001027)  相似文献   

12.
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers.  相似文献   

13.
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which (i) lim sup n→∞ ||Sn||/an〈∞ a.s.and ∞ ∑n=1(1/n)P(||Sn||/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞) are equivalent; (ii) For all constants λ ∈ [0, ∞), lim sup ||Sn||/an =λ a.s.and ^∞∑ n=1(1/n) P(||Sn||/an ≥ε){〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables.  相似文献   

14.
This paper concerns the problem of average σ-width of Sobolev-Wiener classes W^rpq(R^d),W^rpq(M,R^d),and Besov-Wiener classes S^rpqθb(R^d).S^rpqθB(R^d),S^rpqθb(M,R^d),S^rpqθB(R^d)in the metric Lq(R^d) for 1≤q≤p≤∞.The weak asymptotic results concerning the average linear widths,the average Bernstein widths and the infinite-dimensional Gel‘fand widths are obtained,respectively.  相似文献   

15.
Let , be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter in , the ultraproduct of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type , an intermediate K?the space between and being a purely atomic measure space, and a K?the function space K3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅. The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group 03/050.  相似文献   

16.
In this paper, we prove that the weak solutions u∈Wloc^1, p (Ω) (1 〈p〈∞) of the following equation with vanishing mean oscillation coefficients A(x): -div[(A(x)△↓u·△↓u)p-2/2 A(x)△↓u+│F(x)│^p-2 F(x)]=B(x, u, △↓u), belong to Wloc^1, q (Ω)(A↓q∈(p, ∞), provided F ∈ Lloc^q(Ω) and B(x, u, h) satisfies proper growth conditions where Ω ∪→R^N(N≥2) is a bounded open set, A(x)=(A^ij(x)) N×N is a symmetric matrix function.  相似文献   

17.
  We obtain a new sharp inequality for the local norms of functions x ∈ L ∞, ∞ r (R), namely,
where φ r is the perfect Euler spline, on the segment [a, b] of monotonicity of x for q ≥ 1 and for arbitrary q > 0 in the case where r = 2 or r = 3. As a corollary, we prove the well-known Ligun inequality for periodic functions x ∈ L r , namely,
for q ∈ [0, 1) in the case where r = 2 or r = 3. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1338–1349, October, 2008.  相似文献   

18.
A Note on Certain Block Spaces on the Unit Sphere   总被引:1,自引:0,他引:1  
In this note, we clarify a relation between block spaces and the Hardy space. We obtain Bq^0.v belong to H^1(S^n-1)+L(ln+L)^1+v(s^n-1),v〉-1,q〉1,Furthermore,if v≥ 0, q 〉 1. we verify that block spaces Rq^0.v(S^n-1)are proper subspaces of H1 (S^n- 1),  相似文献   

19.
Let D be an increasing sequence of positive integers, and consider the divisor functions: d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1, where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D).  相似文献   

20.
Some new oscillation criteria for nonlinear delay difference equation with damping △^2xn+pn△xn+F(n,x(n-τ,△x(n-σ)=0,n=0,1,2,…,(*)are given. Our results partially solve the open problem posed in [Math. Bohemica, 125 (2000), 421- 430]. Also, we will establish some new oscillation criteria for special cases of (*), which improve some of the well-known results in the literature.  相似文献   

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