二维具间接信号产出趋化模型整体解的有界性

Boundedness of Classical Solutions in the Two-Dimensional Chemotaxis Model with Indirect Signal Production

二维空间中,研究一个山松甲壳虫扩散和聚集行为的完全抛物型趋化模型的整体解的一致有界性.该模型包含三个未知量:飞行甲壳虫的密度、做窝甲壳虫的密度以及由做窝甲壳虫产生的信号浓度.论证过程利用先验估计技巧和耦合估计的方法,并多次使用Gagliardo-Nirenberg不等式和Young不等式等一步步提高解的正则性,最后利用Moser迭代得到结论.证明了当飞行的甲壳虫初始细胞质量小于某个临界值时,该模型整体解是一致有界的。进一步优化了已有结论的条件:该结论去掉了关于做窝甲壳虫的死亡率参数的下界的要求.

The boundedness of global classical solutions of a fully parabolic chemotaxis model describing the diffusion and aggregation of the Mountain Pine Beetle is considered in two dimensions.This model contains three unknowns:the density of the flying Mountain Pine Beetle,the density of the nest Mountain Pine Beetle and the concentration of chemical signal secreted by the nest Mountain Pine Beetle.The proof is based on some a priori estimate techniques and coupled estimation methods.The regularity of the solution is improved step by step by employing the Gagliardo-Nirenberg inequality and Young inequality.Finally,the conclusions are obtained using the Moser iteration.It is shown that this model admits a global classical solution that is uniformly-in-time bounded whenever the initial mass of the flying Mountain Pine Beetle is less than a critical mass.The conditions of the existing conclusion are further optimized:the conclusion of this paper removes the requirement for the lower bound on the mortality parameters of the nest Mountain Pine Beetle.