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991.
Hiroaki Aikawa Tero Kilpeläinen Nageswari Shanmugalingam Xiao Zhong 《Potential Analysis》2007,26(3):281-301
We establish a scale-invariant version of the boundary Harnack principle for p-harmonic functions in Euclidean C
1,1-domains and obtain estimates for the decay rates of positive p-harmonic functions vanishing on a segment of the boundary in terms of the distance to the boundary. We use these estimates
to study the behavior of conformal Martin kernel functions and positive p-superharmonic functions near the boundary of the domain.
H. A. was partially supported by Grant-in-Aid for (B) (2) (No. 15340046) Japan Society for the Promotion of Science. N. S.
was partially supported by NSF grant DMS-0355027. X. Z. was partially supported by the Taft foundation. 相似文献
992.
993.
Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions 总被引:2,自引:0,他引:2
Jianming Liu 《高等学校计算数学学报(英文版)》2007,16(2):97-111
In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method. 相似文献
994.
混合单调算子的两点拉伸型不动点定理 总被引:5,自引:0,他引:5
本文首次提出了混合单调算子不动点的两点拉伸型条件.同时,利用锥映象的不动点指数理论建立了一类特殊的两点拉伸型混合单调算子的不动点存在性定理,并将所得结论应用于带有超线性项的积分方程与微分方程上,得到了新的结论.因而在本质上推进了混合单调算子不动点问题的研究. 相似文献
995.
Wei Lin 《Journal of Mathematical Analysis and Applications》2007,332(1):709-726
In this paper, the initial value problem for a class of fractional differential equations is discussed, which generalizes the existent result to a wide class of fractional differential equations. Also the theoretical result established in the paper ensures the validity of chaos control of fractional differential equations. In particular, feed-back control of chaotic fractional differential equation is theoretically investigated and the fractional Lorenz system as a numerical example is further provided to verify the analytical result. 相似文献
996.
赵雅明 《纯粹数学与应用数学》1997,13(2):99-103
在正交增量的随机积分基础上,利用Lipschitz条件,讨论了下面一类两参数随机积分方程解的唯一性。X(s,t)=Z(s,0)+Z(0,t)-Z(0,0)+∫Rstα(u,v,X)dMuv+∫Rstβ(u,v,X)dmuv+∫R^stγ1(u,v,u',v',X)dMuvdMu'v'+∫R^2stγ2(u,v,u',v',X)dMuvdmu'v'+∫R^2stγ3(u,v,u',v',X)dmuv 相似文献
997.
Andreas Poullikkas Andreas Karageorghis Georgios Georgiou John Ascough 《Numerical Methods for Partial Differential Equations》1998,14(5):667-678
We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667–678, 1998 相似文献
998.
Potential Analysis - Assume that a bounded domain Ω??N (N ≥ 2) has the property that there exists a signed measure µ with compact support in Ω such that, for every... 相似文献
999.
Martin Schechter 《Mathematische Nachrichten》1997,183(1):201-210
We study semilinear problems in which the nonlinear part is linear at infinity but behaves like a function intersecting many of the eigenvalues of the linear operator. The asymptotic linear operator can have a null space of any finite dimension. 相似文献
1000.
In the present investigation, a Fourier analysis is used to study the phase and group speeds of a linearized, two‐dimensional shallow water equations, in a non‐orthogonal boundary‐fitted co‐ordinate system. The phase and group speeds for the spatially discretized equations, using the second‐order scheme in an Arakawa C grid, are calculated for grids with varying degrees of non‐orthogonality and compared with those obtained from the continuous case. The spatially discrete system is seen to be slightly dispersive, with the degree of dispersivity increasing with an decrease in the grid non‐orthogonality angle or decrease in grid resolution and this is in agreement with the conclusions reached by Sankaranarayanan and Spaulding (J. Comput. Phys., 2003; 184 : 299–320). The stability condition for the non‐orthogonal case is satisfied even when the grid non‐orthogonality angle, is as low as 30° for the Crank Nicolson and three‐time level schemes. A two‐dimensional wave deformation analysis, based on complex propagation factor developed by Leendertse (Report RM‐5294‐PR, The Rand Corp., Santa Monica, CA, 1967), is used to estimate the amplitude and phase errors of the two‐time level Crank–Nicolson scheme. There is no dissipation in the amplitude of the solution. However, the phase error is found to increase, as the grid angle decreases for a constant Courant number, and increases as Courant number increases. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献