The cost of approximate controllability for semilinear heat equations in one space dimension
نویسنده
چکیده
In this paper, we apply a successful combination of three key tools which allows to get a measure of the cost of the approximate controllability for semilinear heat equation. The first tool consists to get enough information about the approximate control for the linear heat equation with a potential depending on space-time variable. Then a fixed point method is applied. The fixed point technique described here was previously used in [ Z] to prove the exact controllability for semilinear wave equation in one dimension. The last tool, usually used for control problem (see [ FCZ2, p.589] e.g.), consists to choose adequately the time of controllability.
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