Local existence and global nonexistence theorems for a damped nonlinear hyperbolic equation

The existence and uniqueness of the local generalized solution to the initial boundary value problem for the three-dimensional damped nonlinear hyperbolic equation

     

Quasi-steady-state approximation for a reaction-diffusion system with fast intermediate

We consider a prototype reaction-diffusion system which models a network of two consecutive reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L², as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L²-approach to reaction-diffusion systems having at most quadratic reaction terms, with local L^∞-bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.     

Strong solutions to the Keller‐Segel system with the weak Ln /2 initial data and its application to the blow‐up rate

We shall show an exact time interval for the existence of local strong solutions to the Keller‐Segel system with the initial data u₀ in L^{n /2}_w (?ⁿ), the weak L^{n /2}‐space on ?ⁿ. If ‖u₀‖ is sufficiently small, then our solution exists globally in time. Our motivation to construct solutions in L^{n /2}_w (?ⁿ) stems from obtaining a self‐similar solution which does not belong to any usual L^p(?ⁿ). Furthermore, the characterization of local existence of solutions gives us an explicit blow‐up rate of ‖u (t)‖ for n /2 < p < ∞ as t → T_max, where T_max denotes the maximal existence time (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

实行BOPS模式是否总是有益的？与传统双渠道的对比研究

针对企业线上线下渠道融合战略中提出的BOPS(buy-online-and-pick-up-in-store)模式,在集中式和分散式两情境下分别构建并对比了BOPS和传统双渠道模型,探讨了在传统双渠道基础之上引入BOPS服务是否对企业而言总是有好处的,并分析了传统型消费者占比和消费者的服务敏感性程度对企业实施BOPS的影响。研究表明,企业是否在传统双渠道模式基础上增设BOPS服务,取决于市场中传统型消费者占比规模(即偏好传统零售的消费者)以及各类型消费者对线下服务的敏感性程度;BOPS模式下,当消费者BOPS行为的真正动机是出于欲体验线下零售服务时,对实施BOPS的制造商企业而言更为有利;同时,企业的产品定价和线下服务水平不仅需要考量生产、服务成本,同样需对消费者的服务敏感性有准确的了解和定位。     

Blow‐up of solution of wave equation with internal and boundary source term and non‐porous viscoelastic acoustic boundary conditions

In this paper we study the blow‐up of solution of a mixed problem associated to a nonlinear wave equation with dissipative and source term in a bounded domain of . On a boundary portion of the domain we consider a non‐porous viscoelastic acoustic boundary conditions to a non‐locally reacting boundary.     

Strong solutions to the incompressible magnetohydrodynamic equations

In this paper, we are concerned with strong solutions to the Cauchy problem for the incompressible Magnetohydrodynamic equations. By the Galerkin method, energy method and the domain expansion technique, we prove the local existence of unique strong solutions for general initial data, develop a blow‐up criterion for local strong solutions and prove the global existence of strong solutions under the smallness assumption of initial data. The initial data are assumed to satisfy a natural compatibility condition and allow vacuum to exist. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite and infinite-horizon single vehicle routing problems with a predefined customer sequence and pickup and delivery

We consider the problem of finding the optimal routing of a single vehicle that starts its route from a depot and picks up from and delivers K different products to N customers that are served according to a predefined customer sequence. The vehicle is allowed during its route to return to the depot to unload returned products and restock with new products. The items of all products are of the same size. For each customer the demands for the products that are delivered by the vehicle and the quantity of the products that is returned to the vehicle are discrete random variables with known joint distribution. Under a suitable cost structure, it is shown that the optimal policy that serves all customers has a specific threshold-type structure. We also study a corresponding infinite-time horizon problem in which the service of the customers is not completed when the last customer has been serviced but it continues indefinitely with the same customer order. For each customer, the joint distribution of the quantities that are delivered and the quantity that is picked up is the same at each cycle. The discounted-cost optimal policy and the average-cost optimal policy have the same structure as the optimal policy in the finite-horizon problem. Numerical results are given that illustrate the structural results.     

二维混合层拟序结构的直接数值模拟

本文是在文[1]的基础上,引用Cain等人(1981)提出的映射函数将无穷远的边界变换到有限距离处,用伪谱方法对N-S方程组进行直接数值模拟,研究时间发展的二维混合层的不稳定性,再现了大涡的卷起,涡对的合并与撕裂以及三个涡、四个涡之间的相互作用过程,并将过程进行了动态显示。     

Minimal blow‐up masses and existence of solutions for an asymmetric sinh‐Poisson equation

For a sinh‐Poisson type problem with asymmetric exponents of interest in hydrodynamic turbulence, we establish the optimal lower bounds for the blow‐up masses. We apply this result to construct solutions of mountain pass type on two‐dimensional tori.     

Asymptotic behavior of the solutions of maxwell—klein—gordon field equations in 4—dimensional minkowski space

Abstract. This paper studies the asymptotic behavior of the solutions of massive coupled Maxwell—Klein—Gordon field equations in the 4—dimensional Minkowski space for the case of small initial data with charge. The proof relies on gauge invariant energy estimates and geometric properties of the fields equations. The presence of charge together with the mass term in the Klein—Gordon equation are the novelties of this project and provide us with a situation which cannot be accomodated by standard methods such as the conformal transformation. A covariant Lie derivative operator for the Klein—Gordon field is introduced and allows us to handle the most troublesome terms in the error estimates.