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Reports (Research Report) Year : 1997

## Shape Optimization Problem for Heat Equation

Antoine Henrot
• Function : Author
• PersonId : 833598
Jan Sokolowski

#### Abstract

In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the mesure via the mixed type boundary conditions. The existence of a solution for a class of domain optimization problems is shown. We also investigate the behaviour of the optimal solution for some time $T$, when $T\to\infty$ and we prove that it converges to the optimal solution of the stationary problem. The first order necessary optimality conditions are derived.

#### Domains

Computer Science [cs] Other [cs.OH]

### Dates and versions

inria-00073504 , version 1 (24-05-2006)

### Identifiers

• HAL Id : inria-00073504 , version 1

### Cite

Antoine Henrot, Jan Sokolowski. Shape Optimization Problem for Heat Equation. [Research Report] RR-3185, INRIA. 1997, pp.23. ⟨inria-00073504⟩

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