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.
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.
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
