Optimal Control Problem for Bianchi Equation in Variable Exponent Sobolev Spaces
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In this paper, a necessary and sufficient condition, such as the Pontryagin’s maximum principle for an optimal control problem with distributed parameters, is given by the third-order Bianchi equation with coefficients from variable exponent Lebesgue spaces. The statement of an optimal control problem is studied by using a new version of the increment method that essentially uses the concept of the adjoint equation of the integral form.
Keywords3D optimal control Pontryagin’s maximum principle Bianchi equation Goursat problem Variable exponent Sobolev spaces
Mathematics Subject Classification37D30 49B20 49K20
The authors thank the anonymous reviewers for their careful reading of our manuscript and their valuable comments and suggestions, which helped to improve the manuscript. The research of R. Bandaliyev and V.S. Guliyev was partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number: 02.a03.21.0008) and by the Grant of Presidium of Azerbaijan National Academy of Science 2015.
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