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71.
L. E. Payne G. A. Philippin V. Proytcheva 《Mathematical Methods in the Applied Sciences》2007,30(15):1885-1898
In this paper, we investigate the continuous dependence on the geometry and the initial time for solutions u( x , t) of a class of nonlinear parabolic initial‐boundary value problems. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
72.
Yang Zuosheng 《国际流体数值方法杂志》2005,47(12):1423-1430
A complete boundary integral formulation for compressible Navier–Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for wall pressure and wall skin friction of two‐dimensional compressible laminar viscous flow around airfoils are in good agreement with field numerical methods. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
73.
We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p-adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems. 相似文献
74.
Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions. 相似文献
75.
Kiyoshi Mochizuki 《Journal of Mathematical Analysis and Applications》2007,326(1):582-588
We show that the energy of solutions to the initial boundary value problem for the wave equation in exterior domains with a dissipation which is localized only near infinity tends to zero as the time goes to infinity. We do not make any geometrical condition like star-shapedness on the boundary. 相似文献
76.
WU Ke ZHAO Weizhong & GUO Hanying Department of Mathematics Capital Normal University Beijing China Institute of Theoretical Physics Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2006,(11)
In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems. 相似文献
77.
We present integral-type Darboux transformation for the mKdV hierarchy and for the mKdV hierarchy withself-consistent sources. In contrast with the normal Darboux transformation, the integral-type Darboux transformationscan offer non-auto-Backlund transformation between two (2n 1)-th mKdV equations with self-consistent sources withdifferent degrees. This kind of Darboux transformation enables us to construct the N-soliton solution for the mKdVhierarchy with self-consistent sources. We also propose the formulas for the m times repeated integral-type Darbouxtransformations for both mKdV hierarchy and mKdV hierarchy with self-consistent sources. 相似文献
78.
Based on the theory of calculus of variation, some suffcient conditions are given for some Euler-Lagrangcequations to be equivalently represented by finite or even infinite many Hamiltonian canonical equations. Meanwhile,some further applications for equations such as the KdV equation, MKdV equation, the general linear Euler Lagrangeequation and the cylindric shell equations are given. 相似文献
79.
S. P. Popov 《Computational Mathematics and Mathematical Physics》2006,46(6):983-994
Numerical solutions to three systems of integrable evolutionary equations from the Toda lattice hierarchy are analyzed. These are the classical Toda lattice, the second local dispersive flow, and the second extended dispersive flow. Special attention is given to the properties of soliton solutions. For the equations of the second local flow, two types of solitons interacting in a special manner are found. Solutions corresponding to various initial data are qualitatively outlined. 相似文献
80.