The null boundary controllability for the Mullins equation with periodic boundary conditions

An International Journal of Optimization and Control: Theories & Applications

article

Isil Oner¹ 

[1] Department of Mathematics in Faculty of Science, Gebze Technical University

关键词: Null controllability;    Mullins equation;    moment method;    periodic boundary condiition;    One-dimensional fourth order parabolic equations.;   

DOI  :  10.11121/ijocta.2023.1283

学科分类：地球科学(综合)

来源: Balikesir University

【 摘 要 】

In this paper, we study the null controllability of the Mullins equation with the control acting on the periodic boundary. Firstly, using the duality relation between controllability and observability, we express the controllability condition in terms of the solution of the backward adjoint system. After showing the existence and uniqueness of the solution of the adjoint system, we determine the admissible initial data class since the system is not always controllable under these boundary conditions. Finally, using this spectral analysis, we reduce the null controllability problem to the moment problem and solve the problem on this admissible initial class.

【 授权许可】

CC BY