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**Nassar H. S. Haidar**

Center for Research in Applied Mathematics and Statistics

AUL, Cola Str., Beirut, Lebanon

The boundary value approach to dynamic optimization is still an active area of research in many domains of process engineering. The particular domain of interest in the present work is a certain nonlinear optimization problem, constrained by a 3D neutron diffusion partial differential equation (PDE) and controlled, in time, by the boundary conditions. An analytical solution to the associated linear boundary value problem (BVP), which is a principal activity of this optimization, has been reached in 2019 by this author, based on application of an additive separation of variables (ASOV) principle, and was published in the International Journal of Dynamical Systems and Differential Equations. The sole objective of this paper is to examine and verify the consistency of the ASOV method in solving the BVP of this optimization process. The justification of this method is based on reversibility of a pertaining generalized Euclidean transformation, and on asserting this reversibility in the context of an exterior differential framework for the BVP.

- additive separation of variables
- boundary value problem
- cancer therapy
- dynamical neutron diffusion
- Euclidean transformation
- exterior analysis

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