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Published on 22 Jul 2024

Observability inequalities for the heat equation in an exterior domain with Neumann boundary conditions

In this paper we establish an observability inequality for the heat equation with Neumann boundary conditions in exterior domains. We overcome the difficulties of Neumann boundary conditions and exterior domains by constructing a new method whose spirit is derived from combines Carleman commutator estimates and the parabolic frequency function method. As an immediate application, we show that the null controllability holds for the semilinear heat equations with Neumann boundary conditions in exterior domains.