摘要：
In this paper, we study the L<sup>p</sup> (2 [less-than or equal to] p [less-than or equal to] + infinity ) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x, t), u(x, t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (v over-bar (x, t), u over-bar (x, t)) governed by the classical Darcy's law provided that the corresponding prescribed initial error function (W<sub>0</sub>(X), Z<sub>0</sub>(X)) lies in (H<sup>3</sup> ×H<sup>2</sup>) ( [double-struck R] ) and v<sub>+</sub> - v<sub>-</sub>|+||w<sub>0</sub>||3+||z<sub>0</sub>||<sub>2</sub> is sufficiently small. Furthermore, the L<sup>p</sup> (2 [less-than or equal to] p [less-than or equal to] + infinity ) convergence rates of the solutions are also obtained.
作者机构：
[Li Bo] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
通讯机构：
[Li Bo] H;Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Last exit time;moment;transience;distribution;diffusion process
摘要：
Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex(LBk) < ∞ is proved.
期刊：
Journal of Graph Theory,2006年53(2):83-100 ISSN：0364-9024
通讯作者：
Chen, GT
作者机构：
[Wei, Bing] Department of Mathematics, University of Mississippi, University, MS 38677;[Chen, Guantao] Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303;[Chen, Guantao] Faculty of Mathematics and Statistics, Huazhong Normal University, Wuhan, China;[Shreve, Warren E.] Department of Mathematics, North Dakota State University, Fargo, ND 58105-5075
通讯机构：
[Chen, GT ] ;Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.
关键词：
connectivity;degree;hamiltonian graphs;neighborhood union
期刊：
REVISTA MATEMATICA IBEROAMERICANA,2006年22(2):559-590 ISSN：0213-2230
通讯作者：
Li, Gongbao
作者机构：
[Li, Gongbao; Zheng, Gao-Feng] Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Gongbao] H;Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
asymptotically linear elliptic;exterior domain;algebraic topology argument;positive solution
摘要：
In this paper, we are concerned with the asymptotically linear elliptic problem $-\Delta u+ \lambda_{0}u=f(u), u\in H_{0}^{1}(\Omega ) $ in an exterior domain $\Omega= \mathbb{R}^{N}\setminus\overline{\mathcal{O}} \left( N\geqslant 3\right) $ with $\mathcal{O}$ a smooth bounded and star-shaped open set, and $\lim_{t\rightarrow +\infty }\frac{ f(t)}{t}=l$, $0<l<+\infty$. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2006年16(1):253-277 ISSN：1078-0947
通讯作者：
Duan, RJ
作者机构：
City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China.;City Univ Hong Kong, Liu Bie Ju Ctr Math, Kowloon, Hong Kong, Peoples R China.;Cent China Normal Univ, Dept Math, Lab Nonlinear Anal, Wuhan 430079, Peoples R China.;[Duan, RJ] City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon, Hong Kong, Peoples R China.
通讯机构：
[Duan, RJ] C;City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon, Hong Kong, Peoples R China.
摘要：
In this paper, we study the Cauchy problem for the Boltzmann equation with an external force and the Vlasov-Poisson-Boltzmann system in infinite vacuum. The global existence of solutions is first proved for the Boltzmann equation with an external force which is integrable with respect to time in some sense under the smallness assumption on initial data in weighted norms. For the Vlasov-Poisson-Boltzmann system, the smallness assumption on initial data leads to the decay of the potential field which in turn gives the global existence of solutions by the result on the case with external forces and an iteration argument. The results obtained here generalize those previous works on these topics and they hold for a class of general cross sections including the hard-sphere model.
摘要：
In this paper, we study the issue of uniformity in symmetrical fractional factorial designs. The discrete discrepancy (Biometrika 89 (2002) 893; Metrika 58 (2003) 279; Metrika 60 (2004) 59) is employed as a measure of uniformity. Although there are some emerging literature for connecting uniformity with orthogonality, less attention has been given to this issue for more than three-level fractional factorials and asymmetric fractional factorials. This paper discusses this issue for general symmetric fractional factorials. We derive results connecting uniformity and orthogonality and show that these criteria agree quite well, which provide further justifiable interpretation for some criteria of orthogonality by the consideration of uniformity. In addition, we also point that two measures of orthogonality in the literature (Fang, Hickernell, Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Springer, Berlin, 2002; J. Complexity 19 (2003) 692) are equivalent and derive now a lower bound of the discrete discrepancy. (c) 2004 Elsevier B.V. All rights reserved.
