Optimal distributed control for a new mechanochemical model in biological patterns

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Liu, Changchun¹  Zhang, Xiaoli¹ 

[1] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China

关键词: Mechanochemical model;    Distributed optimal control;    First-order necessary optimality conditions;    Adjoint state system;   

DOI  :  10.1016/j.jmaa.2019.05.057

来源: Elsevier

【 摘 要 】

In this paper, we consider a distributed optimal control problem for the new mechanochemical model in biological patterns which was proposed to describe the dynamics of basal lamina, dermal and epidermal tissues. The model consists of the time-dependent Ginzburg-Landau equation for the concentration difference of at least two pigments phi coupled with the Swift-Hohenberg equation for the difference of dermal cellular densities of at least two types of cells psi. First we prove the existence and uniqueness of a strong solution. The existence of optimal controls is established. Then we prove the control-to-state operator S is Frechet differentiable. Finally we derive the first-order necessary optimality conditions for the optimal control problem. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free