We investigate the existence of an optimal process for such an optimal control problem in which the dynamics is given by the Dirichlet problem driven by weak Laplacian on the Sierpinski gasket. To accomplish this task using a direct variational approach with no global growth conditions on the nonlinear term, we consider the existence of solutions, their uniqueness and their dependence on a functional parameter for mentioned Dirichlet problem. This allows us to prove that the optimal control problem admits at least one solution.
Submitted January 18, 2016. Published April 22, 2016.
Math Subject Classifications: 35J20, 28A80, 49J20.
Key Words: Control problem; Sierpinski gasket; direct variational method; continuous dependence on parameters.
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| Marek Galewski |
Institute of Mathematics
Lodz University of Technology
Wolczanska 215, 90--924 Lodz, Poland
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