Null controllability of linear and semilinear nonlocal heat equations with an additive integral kernel
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Fecha
2019
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Society for Industrial and Applied Mathematics Publications
Resumen
We consider a linear nonlocal heat equation in a bounded domain Ω ⊂ ℝ with Dirichlet boundary conditions. The nonlocality is given by the presence of an integral kernel. We analyze the problem of controllability when the control acts on an open subset of the domain. It is by now known that the system is null controllable when the kernel is time-independent and analytic or, in the one-dimensional case, in separated variables. In this paper, we relax this assumption and we extend the result to a more general class of kernels. Moreover, we get explicit estimates on the cost of null controllability that allow us to extend the result to some semilinear models.
Palabras clave
Carleman inequalities
Heat equation
Linear
Nonlocal terms
Null controllability
Semilinear systems
Heat equation
Linear
Nonlocal terms
Null controllability
Semilinear systems
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Materias
Cita
Biccari, U., & Hernández-Santamaría, V. (2019). Null controllability of linear and semilinear nonlocal heat equations with an additive integral kernel. SIAM Journal on Control and Optimization, 57(4), 2924-2938. https://doi.org/10.1137/18M1218431