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Optimal control of Keller-Segel equations. (English) Zbl 0982.49006
This paper is concerned with an optimal control problem governed by the Keller-Segel equations (partial differential equations). The described techniques for solving such problem are based on the energy estimates and on the compact method. The authors establish a priori estimates for the solutions and they show that the classical method described by J. L. Lions can be used. Existence and uniqueness of local weak solutions are proved. Then existence of optimal controls is justified. Adjoint equations have to be introduced. Note that Keller-Segel equations are introduced to describe the aggregation process of the cellular slime mold by chemical attraction. But this paper only contains theoretical results.
MSC:
49J20Optimal control problems with PDE (existence)
49K20Optimal control problems with PDE (optimality conditions)
92C17Cell movement (chemotaxis, etc.)