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Alexander Chebotarev

Publications and source records attributed to Alexander Chebotarev.

3 recordsLinked to original sources
arXiv2024

Inverse extremal problem for an anti-tumor therapy model

An optimal control problem for a model of tumor growth is studied. In a given subdomain, it is required to minimize the density of tumor cells, while the drug concentration in tissue is limited by given minimal and maximal values. Based on derived estimates of the solution of the controlled system, the solvability of the control problem is proved. The problem is reduced to an optimal control problem with a penalty. An algorithm for solving the optimal control problem with a penalty is constructed and implemented. The efficiency of the algorithm is illustrated by a numerical example.

math.OC↗
arXiv2001

Interaction representation method for Markov master equations in quantum optics

Conditions sufficient for a quantum dynamical semigroup (QDS) to be unital are proved for a class of problems in quantum optics with Hamiltonians which are self-adjoint polynomials of any finite order in creation and annihilation operators. The order of the Hamiltonian may be higher than the order of completely positive part of the formal generator of a QDS. The unital property of a minimal quantum dynamical semigroup implies the uniqueness of the solution of the corresponding Markov master equation in the class of quantum dynamical semigroups and, in the corresponding representation, it ensures preservation of the trace or unit operator. We recall that only in the unital case the formal generator of MME determines uniquely the corresponding QDS.

quant-ph↗