水稻流行性病虫害传播系统的渐近解

在物理防治、生物防治、农业防治等方法综合使用的基础上,为了使用药量确保毒副作用小、水稻安全生产、生产成本小等目标得以实现,建立了水稻流行性病虫害传播系统的数学模型,并用变分迭代、同伦映射等方法求出了其渐近解,真正实现科学地使用农药,从而造福人类。

Existence, uniqueness and stability of positive steady states to a prey-predator diffusion system

In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.

Quasi-neutral limit of the drift-diffusion model for semiconductors with general sign-changing doping profile

The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.