## Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case.(English)Zbl 1106.93010

Summary: This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form $${\partial y\over\partial n} + f(y) = 0$$. We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one has exact controllability to the trajectories.

### MSC:

 93B05 Controllability 35K20 Initial-boundary value problems for second-order parabolic equations 49J20 Existence theories for optimal control problems involving partial differential equations
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### References:

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