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The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems

Authors

  • Jamil A. Ali Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq. https://orcid.org/0000-0002-7225-8030
  • Wissam A. Abdul-Hussien Al-Anbaki Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq. https://orcid.org/0000-0001-5387-4535

DOI:

https://doi.org/10.21123/bsj.2023.7039

Keywords:

Classical Optimal Control, Cost Function, Galerkin Method, Lipschitz continuity, Parabolic Boundary Value Problems.

Abstract

In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

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