UDC 517.9, 519.6
3 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 lyashko.serg@gmail.com
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GENERALIZED OPTIMIZATION OF DRUG TRANSPORT IN TUMORS
Abstract. Optimization and controllability problems for systems described by partial differential equations, where coefficients and the right-hand side belong to different functional spaces, are considered. In particular, pharmacokinetic problems lead to such models. A model described by a general differential equation with zero initial and boundary conditions is analyzed. Coefficients are assumed positive in the area, concentrated sources are modeled by the Dirac delta function. The search of feasible control that minimizes the quality functional is performed. Based on the space of measurable and square integrable functions, adjunction for functions smooth in the research area according to еру norm and conjugate problem are constructed. Negative spaces are introduced for the conjugate problem and generalized solution of the problems is investigated.
Keywords: optimization, controllability, partial differential equations.
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