共查询到20条相似文献,搜索用时 31 毫秒
1.
For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper. 相似文献
2.
The paper is concerned with oscillatory integrals for phase functions having certain de- generate critical points. Under a finite type condition of phase functions we show the estimate of oscillatory integrals of the first kind. The decay of the oscillatory integral depends on indices of the finite type, the spatial dimension and the symbol. 相似文献
3.
This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained. 相似文献
4.
Both oscillatory integral operators and level set operators appear naturally in the study of properties of degenerate Fourier
integral operators (such as generalized Randon transforms). The properties of oscillatory integral operators have a longer
history and are better understood. On the other hand, level set operators, while sharing many common characteristics with
oscillatory integral operators, are easier to handle.
We study L2-estimates on level set operators in dimension two and compare them with what is known about oscillatory integral operators.
The cases include operators with non-degenerate phase functions and the level set version of Melrose-Taylor transform (as
an example of a degenerate phase function). The estimates are formulated in terms of the Newton polyhedra and type conditions. 相似文献
5.
O.Y. Kushel 《Linear algebra and its applications》2011,435(11):2722-2730
A generalization of the definition of an oscillatory matrix based on the theory of cones is given in this paper. The positivity and simplicity of all the eigenvalues of a generalized oscillatory matrix are proved. Classes of generalized even and odd oscillatory matrices are introduced. Spectral properties of the obtained matrices are studied. Criteria of generalized even and odd oscillation are given. Examples of generalized even and odd oscillatory matrices are presented. 相似文献
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L2 estimates are obtained for some oscillatory singular integral operators with analytic phrases by using the technology of almost orthogonality, oscillatory estimates and size estimates. 相似文献
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9.
Thomas Y. Hou 《纯数学与应用数学通讯》1988,41(4):471-495
The behavior of multi-dimensional discrete Boltzmann systems with highly oscillatory data is studied. Homogenized equations for the mean solutions are obtained. Uniform convergence of the oscillatory solutions of the discrete Boltzmann equations to the solutions of the corresponding homogenized equations is established. Moreover, we find that the weak limits of the oscillatory solutions for a model of Broadwell type are not continuous functions of the discrete velocities. Generalization of the above results to problems with multiple-scale initial data is also established. 相似文献
10.
In this paper, we analyze oscillatory properties of perturbed half-linear differential equations (i.e., equations with one-dimensional p-Laplacian). The presented research covers the Euler and Riemann–Weber type equations with very general coefficients. We prove an oscillatory result and a nonoscillatory one, which show that the studied equations are conditionally oscillatory (i.e., there exists a certain threshold value that separates oscillatory and nonoscillatory equations). The obtained criteria are easy to use. Since the number of perturbations is arbitrary, we solve the oscillation behavior of the equations in the critical setting when the coefficients give exactly the threshold value. The results are new for linear equations as well. 相似文献
11.
We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second‐order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation, monotonicity of nonlinearity, and we establish global existence of oscillatory solutions without assuming it a priori. Furthermore, as our example demonstrates, existence of bounded oscillatory solutions does not exclude existence of unbounded nonoscillatory solutions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
In this paper, we deal with oscillatory and asymptotic properties of solutions of a fourth order sub-linear differential equation with the oscillatory operator. We establish conditions for the nonexistence of positive and bounded solutions and an oscillation criterion. 相似文献
13.
Ahmad Al-Salman 《Journal of Mathematical Analysis and Applications》2004,299(1):72-88
In this paper, we study a classes of oscillatory singular integral operators of nonconvolution type with phases more general than polynomials. We prove that such operators are bounded on Lp provided their kernels satisfy a very weak condition. In addition, we also study the related truncated oscillatory singular integral operators. Moreover, we present a class of unbounded oscillatory singular integral operators. 相似文献
14.
Sheehan Olver 《BIT Numerical Mathematics》2010,50(1):149-171
We present a numerically stable way to compute oscillatory integrals. For each additional frequency, only a small, well-conditioned
linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases.
Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the first stable algorithm
for oscillatory integrals with stationary points which does not lose accuracy as the frequency increases and does not require
deformation into the complex plane. 相似文献
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本研究分段常数变量线性中立型泛函微分方程的振动性。用不同的方法研究所考虑的方程,获得存在振动解的两个判定定理。 相似文献
17.
José M. Ferreira Sandra Pinelas 《Journal of Mathematical Analysis and Applications》2003,285(2):506-527
This note is concerned with the oscillatory behavior of a linear retarded system. Several criteria are obtained for having the system oscillatory. Conditions regarding the existence of nonoscillatory solutions are also given. 相似文献
18.
1IntroductionTheexistence,uniqueness,oscillatoryandasymptoticbehaviorofsolutionsofthefirstorderdifferentialequationswithpiecewiseconstantdelayhavebeenstudiedin[1-4].Butoscillatoryandasymptoticbehavioroffirstorderneutraldifferentialequationwithpiecewiseconstantdelayseemtoberarelyconsidered[5,6].Inthispaper,weconsidertheoscillatoryandasymptoticbehavioroffirstordernonlinearneutraldifferentialequationwithpiecewiseconstantdeviatingargumentsoftheformwherecisaconstant,p(t)EC[0, co),fEC(R,R)andxf(x)… 相似文献
19.
This paper devotes to study the oscillatory behavior of solutions of a first order nonlinear impulsive differential equation with mixed argument. First, without assuming the deviating argument to be retarded or advanced, a sufficient condition is established for all solutions of the differential equation to be oscillatory. Next, a sufficient condition for the differential equation to have nonoscillatoty solution is given. Finally, a sufficient and necessary condition for all solutions of the differential equation to be oscillatory is obtained. 相似文献
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