一类具有一般logistic源的高维生物趋化模型整体解的有界性

Global Boundedness of Classical Solutions to a High-dimensional Chemotaxis Model with Generalized Logistic Source

考虑一个具有一般logistic源的高维山地松甲虫的扩散和聚集趋化模型,模型由两个扩散反应方程和一个常微分方程构成.通过G-N不等式讨论模型中系数之间的关系,再利用能量估计的方法证明在非负初值和充分光滑的齐次Neumman边界的条件下,模型的整体解一致存在且有界.

A chemotaxis model with generalized logistic source describes the diffusion and aggregation of the Mountain Pine Beetle(MPB).The model consists of two reaction-diffusion equations and an ordinary differential equation.Through the G-N inequality discuss the relationship between a few coefficients in the model and the method of energy estimation is shown that the model admits global solution for homogeneous Neumann boundary conditions and non-negative initial data,which excludes the possibility offinite-time blow-up.