The singularly perturbed initial boudary value problem for the nonlocal reaction diffusion systems was considered. Using iteration method the comparison theorem was obtained. Introducing stretched variable the formal ...The singularly perturbed initial boudary value problem for the nonlocal reaction diffusion systems was considered. Using iteration method the comparison theorem was obtained. Introducing stretched variable the formal asymptotic solution was constructed. And the existence and its asymptotic behavior of solution for the problem were studied by using the method of the upper and lower solution.展开更多
An analytical model was developed to describe Si？As alloy solidification in the whole range of measured interface velocity. It is demonstrated that at low interface velocity, the solidification occurs in the initial ...An analytical model was developed to describe Si？As alloy solidification in the whole range of measured interface velocity. It is demonstrated that at low interface velocity, the solidification occurs in the initial transient regime. The model leads to good comparison with the experimental data taking both local nonequilibrium effects at high interface velocity and steady state effects at low interface velocity into account. The local nonequilibrium diffusion effects shrink the initial transient period and lead to diffusionless solidification at high interface velocity.展开更多
In this article, we consider a reaction-diffusion differential equation with initial value conditions u（x, 0） =0 on [0, a] and boundary condition ux＋αiu= 0 on Γ={0, α}× （0, T）, and the quenching happens f...In this article, we consider a reaction-diffusion differential equation with initial value conditions u（x, 0） =0 on [0, a] and boundary condition ux＋αiu= 0 on Γ={0, α}× （0, T）, and the quenching happens for the reaction-diffusion equation.展开更多
This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.
This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar...This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t →∞. The convergence is uniform in Rn. Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system.展开更多
Initial value sensitivity in technology diffusion, an important problem for firms＇ decision making such as the timing and target market chosen for new technology or product entering the market, has long been limited ...Initial value sensitivity in technology diffusion, an important problem for firms＇ decision making such as the timing and target market chosen for new technology or product entering the market, has long been limited by the research methodology and tool. Based on the network extension of Bass model, this paper proposes a stochastic threshold model and uses computer simulation to empirically examine three propositions on initial value sensitivity in technology diffusion process. Our findings suggest that diffusion extent is sensitive to not only the number of initial adopters but also their positions in social network, and the variance of customers＇ initial assessment as well, which can be detailed as follows： （1） the degree of technology diffusion exhibits highly positive relation to initial adopter quantity, in particular, when the quantity of initial adopters is small, diffusion extent is very sensitive; （2） diffusion extent is sensitive to the positions of initial adopters; （3） in addition, the variance of customers＇ initial evaluation displays strong negative relation to the final diffusion degree in that the larger variance, the lower of diffusion extent.展开更多
文摘The singularly perturbed initial boudary value problem for the nonlocal reaction diffusion systems was considered. Using iteration method the comparison theorem was obtained. Introducing stretched variable the formal asymptotic solution was constructed. And the existence and its asymptotic behavior of solution for the problem were studied by using the method of the upper and lower solution.
基金partially supported by RFBR, research project No. 14-48-03535
文摘An analytical model was developed to describe Si？As alloy solidification in the whole range of measured interface velocity. It is demonstrated that at low interface velocity, the solidification occurs in the initial transient regime. The model leads to good comparison with the experimental data taking both local nonequilibrium effects at high interface velocity and steady state effects at low interface velocity into account. The local nonequilibrium diffusion effects shrink the initial transient period and lead to diffusionless solidification at high interface velocity.
文摘In this article, we consider a reaction-diffusion differential equation with initial value conditions u（x, 0） =0 on [0, a] and boundary condition ux＋αiu= 0 on Γ={0, α}× （0, T）, and the quenching happens for the reaction-diffusion equation.
基金Supported the National Natural Science Foundation of China（10471080） Supported by the Natural Science Foundation of Henan Province（2004110008）
文摘This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.
文摘This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t →∞. The convergence is uniform in Rn. Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system.
文摘Initial value sensitivity in technology diffusion, an important problem for firms＇ decision making such as the timing and target market chosen for new technology or product entering the market, has long been limited by the research methodology and tool. Based on the network extension of Bass model, this paper proposes a stochastic threshold model and uses computer simulation to empirically examine three propositions on initial value sensitivity in technology diffusion process. Our findings suggest that diffusion extent is sensitive to not only the number of initial adopters but also their positions in social network, and the variance of customers＇ initial assessment as well, which can be detailed as follows： （1） the degree of technology diffusion exhibits highly positive relation to initial adopter quantity, in particular, when the quantity of initial adopters is small, diffusion extent is very sensitive; （2） diffusion extent is sensitive to the positions of initial adopters; （3） in addition, the variance of customers＇ initial evaluation displays strong negative relation to the final diffusion degree in that the larger variance, the lower of diffusion extent.
