On boundary control of the Poisson equation with the third boundary condition

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Mohammed, Alip¹  Tuffaha, Amjad² 

[1] Khalifah Univ Sci & Technol, Petr Inst, CAS, Dept Math, Abu Dhabi, U Arab Emirates

[2] Amer Univ Sharjah, Dept Math & Stat, Sharjah, U Arab Emirates

关键词: Optimal control;    Boundary control;    Boundary eigenvalue problem;    The third boundary condition with complex valued constant coefficient;    Poisson equation;   

DOI  :  10.1016/j.jmaa.2017.10.059

来源: Elsevier

【 摘 要 】

This paper studies controllability of the Poisson equation on the unit disk in C subject to the third boundary condition when the control is imposed on the boundary. We use complex analytic methods to prove existence and uniqueness of the control when the parameter A is a nonzero complex number but not a negative integer (not an eigenvalue). Otherwise, due to multiplicity of solutions to the underlying problem, when A is a negative integer, controllability could only be obtained if proper additional conditions on the boundary are imposed. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free