Dynamical shape control of the heat equaion (Q1117450)
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scientific article; zbMATH DE number 4092210
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dynamical shape control of the heat equaion |
scientific article; zbMATH DE number 4092210 |
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Dynamical shape control of the heat equaion (English)
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1989
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An optimal control problem for a system described by a one-dimensional heat equation in a non-cylindrical domain with moving boundary is considered. The optimization problem is to find the evolution of the moving boundary in such a way that the total dissipated energy of the system is minimal. The existence of an optimal control is proved. Using the dynamic programming approach it is shown that the related Hamilton-Jacobi equation has a unique generalized viscosity solution given by the value function of the original optimal control problem.
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minimal dissipated energy
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non-cylindrical domain
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moving boundary
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Hamilton-Jacobi equation
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unique generalized viscosity solution
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value function
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