Control of the Cauchy problem on Hilbert spaces : a global approach via symbol criteria
- Author
- Duvan Cardona Sanchez (UGent) , Julio Delgado, Brian Grajales and Michael Ruzhansky (UGent)
- Organization
- Project
- Abstract
- Let A and B be invariant linear operators with respect to a decomposition {H-j}(j is an element of N) of a Hilbert space H in subspaces of finite dimension. We give necessary and sufficient conditions for the controllability of the Cauchy problemu(t) = Au + Bv, u(0) = u(0),in terms of the (global) matrix-valued symbols sigma A and sigma B of A and B, respectively, associated to the decomposition {H-j}(j is an element of N). Then, we present some applications including the controllability of the Cauchy problem on compact manifolds for elliptic operators and the controllability of fractional diffusion models for Ho center dot rmander sub-Laplacians on compact Lie groups. We also give conditions for the controllability of wave and Schro center dot dinger equations in these settings.
- Keywords
- Applied Mathematics, Analysis, Pharmacology (medical), Complementary and alternative medicine, Pharmaceutical Science, Ghent Analysis & PDE center, Control theory, diffusion models, exact controllability, fractional mod-els, controllability cost, PARTIAL-DIFFERENTIAL-EQUATIONS, NULL-CONTROLLABILITY, FRACTIONAL ORDER, HEAT-EQUATION, NODAL SETS, REGULARITY, OPERATORS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01HP4Q0G31BYMEYDMGXYEB9HF5
- MLA
- Cardona Sanchez, Duvan, et al. “Control of the Cauchy Problem on Hilbert Spaces : A Global Approach via Symbol Criteria.” COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, vol. 22, no. 11, 2023, pp. 3295–329, doi:10.3934/cpaa.2023113.
- APA
- Cardona Sanchez, D., Delgado, J., Grajales, B., & Ruzhansky, M. (2023). Control of the Cauchy problem on Hilbert spaces : a global approach via symbol criteria. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 22(11), 3295–3329. https://doi.org/10.3934/cpaa.2023113
- Chicago author-date
- Cardona Sanchez, Duvan, Julio Delgado, Brian Grajales, and Michael Ruzhansky. 2023. “Control of the Cauchy Problem on Hilbert Spaces : A Global Approach via Symbol Criteria.” COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 22 (11): 3295–3329. https://doi.org/10.3934/cpaa.2023113.
- Chicago author-date (all authors)
- Cardona Sanchez, Duvan, Julio Delgado, Brian Grajales, and Michael Ruzhansky. 2023. “Control of the Cauchy Problem on Hilbert Spaces : A Global Approach via Symbol Criteria.” COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 22 (11): 3295–3329. doi:10.3934/cpaa.2023113.
- Vancouver
- 1.Cardona Sanchez D, Delgado J, Grajales B, Ruzhansky M. Control of the Cauchy problem on Hilbert spaces : a global approach via symbol criteria. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. 2023;22(11):3295–329.
- IEEE
- [1]D. Cardona Sanchez, J. Delgado, B. Grajales, and M. Ruzhansky, “Control of the Cauchy problem on Hilbert spaces : a global approach via symbol criteria,” COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, vol. 22, no. 11, pp. 3295–3329, 2023.
@article{01HP4Q0G31BYMEYDMGXYEB9HF5,
abstract = {{Let A and B be invariant linear operators with respect to a decomposition {H-j}(j is an element of N) of a Hilbert space H in subspaces of finite dimension. We give necessary and sufficient conditions for the controllability of the Cauchy problemu(t) = Au + Bv, u(0) = u(0),in terms of the (global) matrix-valued symbols sigma A and sigma B of A and B, respectively, associated to the decomposition {H-j}(j is an element of N). Then, we present some applications including the controllability of the Cauchy problem on compact manifolds for elliptic operators and the controllability of fractional diffusion models for Ho center dot rmander sub-Laplacians on compact Lie groups. We also give conditions for the controllability of wave and Schro center dot dinger equations in these settings.}},
author = {{Cardona Sanchez, Duvan and Delgado, Julio and Grajales, Brian and Ruzhansky, Michael}},
issn = {{1534-0392}},
journal = {{COMMUNICATIONS ON PURE AND APPLIED ANALYSIS}},
keywords = {{Applied Mathematics,Analysis,Pharmacology (medical),Complementary and alternative medicine,Pharmaceutical Science,Ghent Analysis & PDE center,Control theory,diffusion models,exact controllability,fractional mod-els,controllability cost,PARTIAL-DIFFERENTIAL-EQUATIONS,NULL-CONTROLLABILITY,FRACTIONAL ORDER,HEAT-EQUATION,NODAL SETS,REGULARITY,OPERATORS}},
language = {{eng}},
number = {{11}},
pages = {{3295--3329}},
title = {{Control of the Cauchy problem on Hilbert spaces : a global approach via symbol criteria}},
url = {{http://doi.org/10.3934/cpaa.2023113}},
volume = {{22}},
year = {{2023}},
}
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