Some results on controllability for linear and nonlinear heat equations in unbounded domains
By Manuel González-Burgos, Luz de Teresa. Advances in Differential Equations, 2007
57 citations recorded by the source corpus.
In this paper we present some results concerning the null controllability for a heat equation in unbounded domains. We characterize the conditions that must satisfy the auxiliary function that drives to a global Carleman inequality for the adjoint problem and then to get a null controllability result. We give some examples of unbounded domains ( ;!) that satisfy these sucient conditions. Finally, when n! is bounded, we prove the null controllability of the semilinear heat equation when the nonlinearity f(y;ry) grows slower than jyj log 3=2 (1 +jyj +jryj) +jryj log 1=2 (1 +jyj +jryj) at innity (generally in this case in the absence of control, blow up occurs). In this aim we also prove the linear null controllability problem with L 1 -controls.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5cdb1543edad1943f5b5d7ddd3a53977127607fe
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In Computational Theory and Mathematics
- Karine Beauchard
- Roberto Guglielmi
- Raphael Henry
- Bernard Helffer
- Masahiro Yamamoto
- Piermarco Cannarsa
- Enrique Zuazua
- Oleg Yu. Imanuvilov
In Control and Systems Engineering
- Karine Beauchard
- Roberto Guglielmi
- Bernard Helffer
- Raphael Henry
- Masahiro Yamamoto
- Piermarco Cannarsa
- Enrique Zuazua
- Eduardo Cerpa
In Mathematical Physics
- Karine Beauchard
- Roberto Guglielmi
- Bernard Helffer
- Raphael Henry
- Masahiro Yamamoto
- Piermarco Cannarsa
- Oleg Yu. Imanuvilov
- Enrique Zuazua
Citations in the corpus
- Null controllability of Grushin-type operators in dimension two (2011, background): “The null and approximate controllability of the heat equation are essentially well understood subjects for both linear and semilinear equations, and for bounded or unbounded domains (see, for instance, [15], [19], [21], [22], [23], [27], [31], [32], [36], [39], [40], [45], [46]).”
- DEGENERATE PARABOLIC OPERATORS OF KOLMOGOROV TYPE WITH A GEOMETRIC CONTROL CONDITION (2015, background): “1 Null controllability of the heat equation The null and approximate controllabilities of the heat equation are essentially well understood subjects for both linear and semilinear equations, for bounded or unbounded domains [3, 27, 30, 32, 33, 34, 37, 44, 46, 48, 51, 52, 62, 63] and also with discon”
- Carleman estimates for parabolic equations and applications (2009, background): “As very limited references on the basis of the Carleman estimate, we refer to the following papers: (1) Parabolic equations: [37, 55, 56, 63, 64, 127].”