Open Access
| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 73 | |
| Number of page(s) | 30 | |
| DOI | https://doi.org/10.1051/cocv/2025059 | |
| Published online | 29 August 2025 | |
- E. Fernandez-Cara and E. Zuazua, The cost of approximate controllability for heat equations: the linear case. Adv. Differ. Equ. 5 (2000) 465–514. [Google Scholar]
- E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. H. Poincare C Anal. Non Linéaire 17 (2000) 583–616. [Google Scholar]
- L. Miller, Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time. J. Differ. Equ. 204 (2004) 202–226. [Google Scholar]
- T. Duyckaerts, X. Zhang and E. Zuazua, On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials. Ann. Inst. H. Poincareé C Anal. Non Linéaire 25 (2008) 1–41. [Google Scholar]
- V.Z. Meshkov, On the possible rate of decrease at infinity of the solutions of second-order partial differential equations. Mat. Sb. 182 (1991) 364–383. [Google Scholar]
- V.A. Kondratiev and E.M. Landis, Qualitative theory of second-order linear partial differential Equations, in Partial Differential Equations, 3 (Russian), Itogi Nauki i Tekhniki. Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow (1988) 99–215, 220. [Google Scholar]
- A. Logunov, E. Malinnikova, N. Nadirashvili and F. Nazarov, The landis conjecture on exponential decay. arXiv:2007.07034 (2020). [Google Scholar]
- C. Kenig, L. Silvestre and J.-N. Wang, On Landis’ conjecture in the plane. Commun. Part. Differ. Equ. 40 (2015) 766–789. [Google Scholar]
- A.V. Fursikov and O.Y. Imanuvilov, Controllability of evolution equations. Vol. 34 of Lecture Notes Series. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
- H. Donnelly and C. Fefferman, Nodal sets of eigenfunctions on Riemannian manifolds. Invent. Math. 93 (1988) 161–183. [Google Scholar]
- J. Zhu, Quantitative uniqueness of elliptic equations. Amer. J. Math. 138 (2016) 733–762. [Google Scholar]
- J. Bourgain and C.E. Kenig, On localization in the continuous Anderson-Bernoulli model in higher dimension. Invent. Math. 161 (2005) 389–426. [Google Scholar]
- J. Zhu, Quantitative uniqueness of solutions to parabolic equations. J. Funct. Anal. 275 (2018) 2373–2403. [Google Scholar]
- G. Camliyurt and I. Kukavica, Quantitative unique continuation for a parabolic equation. Indiana Univ. Math. J. 67 (2018) 657–678. [Google Scholar]
- J. Zhu and J. Zhuge, Spectral inequality for schrödinger equations with power growth potentials. arXiv:2301.12338 (2023). [Google Scholar]
- E. Zuazua, Controllability and observability of partial differential equations: some results and open problems, in Handbook of Differential Equations: Evolutionary Equations, Vol. III. Handb. Differ. Equ. Elsevier/North-Holland, Amsterdam (2007) 527–621. [Google Scholar]
- E. Fernández-Cara and S. Guerrero, Global Carleman inequalities for parabolic systems and applications to controllability. SIAM J. Control Optim. 45 (2006) 1399–1446. [Google Scholar]
- E. Zuazua, Exact controllability for semilinear wave equations in one space dimension. Ann. Inst. H. Poincaré C Anal. Non Linéaire 10 (1993) 109–129. [Google Scholar]
- K.D. Phung and G. Wang, An observability estimate for parabolic equations from a measurable set in time and its applications. J. Eur. Math. Soc. 15 (2013) 681–703. [CrossRef] [MathSciNet] [Google Scholar]
- L.C. Evans, Partial differential equations. Vol. 19 of Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence, RI (2010). [Google Scholar]
- J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems. SIAM Rev. 30 (1988) 1–68. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Coron, Control and Nonlinearity, Vol. 136. American Mathematical Society (2007). [Google Scholar]
- M. González-Burgos and R. Pérez-García, Controllability results for some nonlinear coupled parabolic systems by one control force. Asymptot. Anal. 46 (2006) 123–162. [Google Scholar]
- E. Fernández-Cara, J. Limaco and S.B. de Menezes, Null controllability for a parabolic equation with nonlocal nonlinearities. Syst. Control Lett. 61 (2012) 107–111. [Google Scholar]
- G.M. Lieberman, Second Order Parabolic Differential Equations. World Scientific Publishing Co., Inc., River Edge, NJ (1996). [Google Scholar]
- E. Malinnikova, Propagation of smallness for solutions of generalized cauchy–riemann systems. Proc. Edinburgh Math. Soc. 47 (2004) 191–204. [Google Scholar]
- Y. Zhu, Propagation of smallness for solutions of elliptic equations in the plane. Math. Eng. 7 (2025) 1–12. [Google Scholar]
- B. Bojarski, Generalized Solutions of a System of Differential Equations of the First Order and Elliptic Type with Discontinuous Coefficients, Vol. 118. Citeseer (2009). [Google Scholar]
- J. Apraiz, L. Escauriaza, G. Wang and C. Zhang, Observability inequalities and measurable sets. J. Eur. Math. Soc. 16 (2014).. [Google Scholar]
- L. Miller, A direct lebeau-robbiano strategy for the observability of heat-like semigroups. Discrete Continuous Dyn. Syst. Ser. B 14 (2010) 1465–1485. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.
