Mathematical analysis on a multidimensional model of morphogen transport with receptor synthesis  

作　　者：Hongwei Yin Xiaoyong Xiao Xiaoqing Wen Tianshou Zhou 

机构地区：[1]School of Science, Nanchang University Nanchang 330031, P. R. China [2]School of Mathematics and Computational Science Sun Yat-Sen University Guangzhou 510275, P. R. China

出　　处：《International Journal of Biomathematics》2014年第5期67-81,共15页生物数学学报（英文版）

摘　　要：In biological development, morphogens are locally produced and spread to other regions in organs, forming gradients that control the inter-related pattern and growth of developing organs. Mechanisms of morphogen transport were built and investigated by numerical simulations in [A. D. Lander, Q. Nie and F. Y. M. Wan, Do morphogen gradients arise by diffusion？ Developmental Cell 2 （2002） 785-796]. In that paper, model C, which considers endocytosis, exocytosis and receptor synthesis and degradation, is in a one-dimensional spatial region and couples a partial differential equation with ordinary differential equations. Here, this model is promoted to an arbitrary dimension bounded region. We prove existence, uniqueness and non-negativity of a global solution for this advanced model, of its steady-state solution and linear stability of steady state by operator semigroup, the Schauder theorem and local perturbation method. Our results improve previous results for this model in a one dimension region.

关 键 词：WELL-POSEDNESS morphogen transport ENDOCYTOSIS receptor synthesis. 

分 类 号：O171[理学—数学] Q959.117[理学—基础数学]