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31.
Heterogeneity is typically the result of space variability of soil parameters at different scales. Soil anisotropy may be defined as the spatial persistence in some direction only, across coarse-grid elements, of heterogeneous structures with different characteristic lengths in different directions. One can account for the effect of these structures by upscaling soil properties. Analyzing flow in a strongly anisotropic structured soil at different scales evidences how transverse dispersion reduces to a subscale process, leading to mixing within the conductive structures. 相似文献
32.
33.
In this paper we focus on the problem of identifying the index sets P(x):=i|xi>0, N(x):={i|Fi(x)>0 and C(x):=i|xi=Fi(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10 相似文献
34.
Patrick Guidotti 《Mathematische Nachrichten》2004,272(1):32-45
We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
35.
考虑非线性时滞差分方程x_{n+1}-x_n+p_nf(x_{n-l_1},x_{n-l_2}x_{n-l_m})=0, n=0,1,2, 获得了方程所有解振动的充分条件, 推广并改进了现有文献中的结果. 相似文献
36.
Luis L. Bonilla 《Journal of statistical physics》1987,46(3-4):659-678
A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered. 相似文献
37.
一类具有非局部反应扩散方程的奇摄动问题 总被引:7,自引:0,他引:7
本文讨论一类具非局部反应扩散方程的奇摄动初始边值问题,利用迭代法及微分不等式,研究了初始边值问题的存在唯一及其渐近性态。 相似文献
38.
Fully and partially observed stochastic control of systems with nonlinear dynamics and terminal and running costs are considered.
Measure changes are introduced which allow both state and observation dynamics to be thought of as linear. In the case when
the terms of the cost have a special form the measure change transformation “cancels out” the nonlinearities and changes the
original nonlinear problem into a classical LQG one and standard results can be applied. We also consider unnormalized conditional
densities of the whole path as state variables and obtain dynamic programming and verification results.
R. J. Elliott wishes to acknowledge support of the Natural Sciences and Engineering Research Council of Canada, Grant A7964. 相似文献
39.
A Modified SQP Method and Its Global Convergence 总被引:6,自引:0,他引:6
Guanglu Zhou 《Journal of Global Optimization》1997,11(2):193-205
The sequential quadratic programming method developed by Wilson, Han andPowell may fail if the quadratic programming subproblems become infeasibleor if the associated sequence of search directions is unbounded. In [1], Hanand Burke give a modification to this method wherein the QP subproblem isaltered in a way which guarantees that the associated constraint region isnonempty and for which a robust convergence theory is established. In thispaper, we give a modification to the QP subproblem and provide a modifiedSQP method. Under some conditions, we prove that the algorithm eitherterminates at a Kuhn–Tucker point within finite steps or generates aninfinite sequence whose every cluster is a Kuhn–Tucker point.Finally, we give some numerical examples. 相似文献
40.
This paper considers a problem of nonlinear programming in which the objective function is the ratio of two linear functions and the constraints define a bounded and connected feasible region. Using a coordinate transformation, this problem is transformed into a simpler one, whose geometric interpretation is of particular significance. The transformation leads to a characterization of some special vertices of the feasible region from both the theoretical and operational points of view. 相似文献