Farag, M. H. On the derivation of discrete conjugate boundary value problem for an optimal control parabolic problem. (English) Zbl 1041.49023 N. Z. J. Math. 32, No. 1, 21-31 (2003). Summary: This paper treats the problem of control of a quasilinear parabolic equation with controls in the coefficients, in the boundary conditions and in the right side of the equation. Necessary optimality conditions in the form of a maximum principle are proved. The difference approximations problem is constructed. Finally, the discrete conjugate boundary value problem for the considered problem is established. MSC: 49K20 Optimality conditions for problems involving partial differential equations 49J20 Existence theories for optimal control problems involving partial differential equations 49M25 Discrete approximations in optimal control 49M30 Other numerical methods in calculus of variations (MSC2010) 49N10 Linear-quadratic optimal control problems Keywords:optimal control; parabolic equations; necessary optimality conditions; finite difference method; stability; discrete conjugate problem PDFBibTeX XMLCite \textit{M. H. Farag}, N. Z. J. Math. 32, No. 1, 21--31 (2003; Zbl 1041.49023)