Ryu, Sang-Uk Optimal control problems governed by some semilinear parabolic equations. (English) Zbl 1054.49002 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 56, No. 2, 241-252 (2004). This paper deals with optimal control associated to nonlinear parabolic equations. After giving some known results the author derives a characterization for the optimal control. Then uniqueness of the optimal control is proved by using the strict convexity of the functional. Application to an optimal control problem governed by Keller-Segel equations is done. No numerical application is treated. Reviewer: Yves Cherruault (Paris) Cited in 12 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations 49K20 Optimality conditions for problems involving partial differential equations Keywords:optimal control; Keller–Segel equations; optimality conditions; uniqueness PDFBibTeX XMLCite \textit{S.-U. Ryu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 56, No. 2, 241--252 (2004; Zbl 1054.49002) Full Text: DOI References: [1] Ahmed, N. U.; Teo, K. L., Optimal Control of Distributed Parameter Systems (1981), North-Holland: North-Holland New York · Zbl 0472.49001 [2] Barbu, V., Analysis and Control of Nonlinear Infinite Dimensional Systems (1993), Academic Press: Academic Press Boston [3] Casas, E.; Fern’andez, L. A.; Yong, J., Optimal control of quasilinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect., 125, 545-565 (1995) · Zbl 0833.49002 [4] R. Dautray, J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 5, Springer, Berlin, 1992.; R. Dautray, J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 5, Springer, Berlin, 1992. · Zbl 0755.35001 [5] Keller, K. L.; Segel, L. A., Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., 26, 399-415 (1970) · Zbl 1170.92306 [6] Lions, J. L., Optimal Control of Systems Governed by Partial Differential Equations (1971), Springer: Springer Berlin · Zbl 0203.09001 [7] Papageorgiou, N. S., On the optimal control of strongly nonlinear evolution equations, J. Math. Anal. Appl., 164, 83-103 (1992) · Zbl 0766.49010 [8] Ryu, S.-U.; Yagi, A., Optimal control of Keller-Segel equations, J. Math. Anal. Appl., 256, 45-66 (2001) · Zbl 0982.49006 [9] Triebel, H., Interpolation Theory, Function Spaces, Differential Operators (1978), North-Holland: North-Holland Amsterdam · Zbl 0387.46032 [10] Zeidler, E., Nonlinear Functional analysis and its Applications. II/B, Nonlinear Monotone Operator (1990), Springer: Springer Berlin This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.