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101.
Giuseppe Maria Coclite 《偏微分方程通讯》2013,38(8):1253-1272
We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L p setting. 相似文献
102.
Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis. 相似文献
103.
In this paper, we are concerned with the behavior of shock waves in a 2 × 2 balance law with discontinuous source terms. We obtain the existence of a local shock wave solution of this problem and deduce that the discontinuous source terms create a weak discontinuity in this solution. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
104.
In this paper, a simultaneous canonical form of a pair of rectangular complex matrices is developed. Using this new tool we give a necessary and sufficient condition to assure that the reverse order law is valid for the weighted Moore–Penrose inverse. Additionally, we characterize matrices ordered by the weighted star partial order and adjacent matrices as applications. 相似文献
105.
Uniform spreading of oil on solid surfaces is important in many processes where proper lubrication is required and this can be controlled using surfactants. The role of oil–solid interfacial self-assembled surfactant structure (SASS) in oil spreading is examined in this study for the case of hexadecane-surfactant droplet spreading on a flat horizontal copper surface, with triphenyl phosphorothionate surfactants having varying chain lengths (0 to 9). It is shown that the frictional forces (FSASS) as determined by the SASS regulate droplet spreading rate according to surfactant chain length; surfactants with longer chains led to higher reduction in the spreading rate. The extent of such forces, FSASS, depends on the surfactant density of the evolving SASS, and specific configuration the evolving SASS exhibit as per the orientations of the surfactant chains therein. Thus, FSASS = [k1 + k2(t)] Γδ(t), where Γδ(t) is the surfactant adsorption density of SASS at time ‘t’ during evolution, and, k1 and k2(t) are the force coefficients for Γδ(t) and orientations (as a function of spreading time) of the surfactant chains respectively. As a SASS evolves/grows along with adsorption of surfactants at the spreading induced fresh interface, the k1Γδ(t) component of FSASS increases and contributes to reduction in the net spreading force (S). With a decrease in the net spreading force, the existence of a cross-over period, during which the transition of the spatial dynamics of the chains from disordered to realignment/packing induced ordered orientation occurs, has been inferred from the FSASS vs. chain length relationships. Such relationships also suggested that the rate of realignment/packing is increased progressively particularly due the realignment/packing induced decrease in the net spreading force. Therefore, the realignment process is a self-induced process, which spans a measurable period of time (several minutes), the cross-over period, during which the net spreading force decreases essentially due to such self-induced process. 相似文献
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考虑一类"中度偏离"单位根过程,y_t=q_ny_t-1+u_t,其中qn=1+c/(k_n),k_n=o(n),c为一非零常数,{u_t}为随机扰动项序列.在允许扰动项方差无穷的条件下,构造q_n的复合分位数估计,并得到了该估计的渐近分布.最后通过数值模拟,在扰动项服从t(2)分布下,说明了该估计的稳健和有效性. 相似文献
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