Fréchet differentiability for a damped sine-Gordon equation (Q1034571)
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scientific article; zbMATH DE number 5626927
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fréchet differentiability for a damped sine-Gordon equation |
scientific article; zbMATH DE number 5626927 |
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Fréchet differentiability for a damped sine-Gordon equation (English)
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6 November 2009
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An initial boundary value problem for the damped sine-Gordon equation with a variable diffusion coefficient is considered. The aim is to identify coefficients in equation such that the solution attains a desired behavior. This leads to an optimal control problem for which the necessary condition of optimality is written in form of a variational inequality. Much effort is done to prove the Gâteaux differentiability of the solution map and the Fréchet differentiability of the objective functional.
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optimal control
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parameter identification
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Fréchet differentiability
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