A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论，研究了Boussinesq方程，通过对Boussinesq方程进行行波变换，得到了相应行波系统的首次积分和平衡点，给出了不同参数条件下的相图，证实了Boussinesq方程存在孤立波解和周期波解。