Burq, Nicolas; Dehman, Belhassen; Le Rousseau, Jérôme Semi-classical observation suffices for observability: wave and Schrödinger equations. (English) Zbl 07815227 ESAIM, Control Optim. Calc. Var. 30, Paper No. 10, 31 p. (2024). MSC: 35L20 35L05 35Q41 93B07 PDFBibTeX XMLCite \textit{N. Burq} et al., ESAIM, Control Optim. Calc. Var. 30, Paper No. 10, 31 p. (2024; Zbl 07815227) Full Text: DOI arXiv
Krieger, Joachim; Xiang, Shengquan Boundary stabilization of the focusing NLKG equation near unstable equilibria: radial case. (English) Zbl 07787348 Pure Appl. Anal. 5, No. 4, 833-894 (2023). MSC: 35B40 35B34 35L71 PDFBibTeX XMLCite \textit{J. Krieger} and \textit{S. Xiang}, Pure Appl. Anal. 5, No. 4, 833--894 (2023; Zbl 07787348) Full Text: DOI arXiv
Akil, Mohammad; Issa, Ibtissam; Wehbe, Ali A N-dimensional elastic\(\backslash\)viscoelastic transmission problem with Kelvin-Voigt damping and non smooth coefficient at the interface. (English) Zbl 1523.35037 S\(\vec{\text{e}}\)MA J. 80, No. 3, 425-462 (2023). MSC: 35B40 35L52 93B52 93C20 PDFBibTeX XMLCite \textit{M. Akil} et al., S\(\vec{\text{e}}\)MA J. 80, No. 3, 425--462 (2023; Zbl 1523.35037) Full Text: DOI arXiv
Louis-Rose, Carole; Tebou, Louis Carleman estimates and simultaneous boundary controllability of uncoupled wave equations. (English) Zbl 07708064 Appl. Math. Optim. 88, No. 2, Paper No. 49, 47 p. (2023). Reviewer: Juan Ramón Torregrosa Sánchez (València) MSC: 93C20 93B05 35L05 35L51 35K05 PDFBibTeX XMLCite \textit{C. Louis-Rose} and \textit{L. Tebou}, Appl. Math. Optim. 88, No. 2, Paper No. 49, 47 p. (2023; Zbl 07708064) Full Text: DOI
Laurent, Camille; Léautaud, Matthieu Uniform observation of semiclassical Schrödinger eigenfunctions on an interval. (English) Zbl 1522.34111 Tunis. J. Math. 5, No. 1, 125-170 (2023). Reviewer: A. S. Makin (Moskva) MSC: 34L40 34L10 93B07 PDFBibTeX XMLCite \textit{C. Laurent} and \textit{M. Léautaud}, Tunis. J. Math. 5, No. 1, 125--170 (2023; Zbl 1522.34111) Full Text: DOI arXiv
Fu, Xiaoyu; Liao, Zhonghua Observability estimate for the wave equation with variable coefficients. (English) Zbl 1498.93060 SIAM J. Control Optim. 60, No. 4, 2344-2372 (2022). MSC: 93B07 93C20 35L05 PDFBibTeX XMLCite \textit{X. Fu} and \textit{Z. Liao}, SIAM J. Control Optim. 60, No. 4, 2344--2372 (2022; Zbl 1498.93060) Full Text: DOI arXiv
Wehbe, Ali; Nasser, Rayan; Noun, Nahla Stability of N-D transmission problem in viscoelasticity with localized Kelvin-Voigt damping under different types of geometric conditions. (English) Zbl 1481.35041 Math. Control Relat. Fields 11, No. 4, 885-904 (2021). MSC: 35B35 35L20 93B52 93C20 PDFBibTeX XMLCite \textit{A. Wehbe} et al., Math. Control Relat. Fields 11, No. 4, 885--904 (2021; Zbl 1481.35041) Full Text: DOI
Jena, Vaibhav Kumar Carleman estimate for ultrahyperbolic operators and improved interior control for wave equations. (English) Zbl 1475.35087 J. Differ. Equations 302, 273-333 (2021). MSC: 35B45 35L20 53C50 93B05 93B07 93B27 PDFBibTeX XMLCite \textit{V. K. Jena}, J. Differ. Equations 302, 273--333 (2021; Zbl 1475.35087) Full Text: DOI arXiv
Chaves-Silva, F. W.; Puel, J.-P.; Santos, M. C. Localization of energy and localized controllability. (English) Zbl 1467.93032 ESAIM, Control Optim. Calc. Var. 27, Paper No. 29, 15 p. (2021). MSC: 93B05 93C20 35J10 PDFBibTeX XMLCite \textit{F. W. Chaves-Silva} et al., ESAIM, Control Optim. Calc. Var. 27, Paper No. 29, 15 p. (2021; Zbl 1467.93032) Full Text: DOI
Tebou, Louis Simultaneous and indirect control of waves: some recent developments and open problems. (English) Zbl 1458.93035 Ammari, Kaïs (ed.) et al., Identification and control: some challenges. Summer school, Monastir, Tunisia, June 18–20, 2019. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 757, 51-90 (2020). MSC: 93B05 93C20 35L05 PDFBibTeX XMLCite \textit{L. Tebou}, Contemp. Math. 757, 51--90 (2020; Zbl 1458.93035) Full Text: DOI
Shao, Arick On controllability of waves and geometric Carleman estimates. (English) Zbl 1479.35552 Sémin. Laurent Schwartz, EDP Appl. 2018-2019, Exp. No. 11, 14 p. (2019). MSC: 35L20 93B05 93B07 PDFBibTeX XMLCite \textit{A. Shao}, Sémin. Laurent Schwartz, EDP Appl. 2018--2019, Exp. No. 11, 14 p. (2019; Zbl 1479.35552) Full Text: DOI
Acosta, Sebastián Recovery of pressure and wave speed for photoacoustic imaging under a condition of relative uncertainty. (English) Zbl 1458.94009 Inverse Probl. 35, No. 11, Article ID 115013, 11 p. (2019). MSC: 94A08 76Q99 92C55 PDFBibTeX XMLCite \textit{S. Acosta}, Inverse Probl. 35, No. 11, Article ID 115013, 11 p. (2019; Zbl 1458.94009) Full Text: DOI arXiv
Waters, Alden Low regularity ray tracing for wave equations with Gaussian beams. (English) Zbl 1418.35349 Rocky Mt. J. Math. 49, No. 3, 1005-1027 (2019). MSC: 35R01 35R30 35L20 58J45 35A22 PDFBibTeX XMLCite \textit{A. Waters}, Rocky Mt. J. Math. 49, No. 3, 1005--1027 (2019; Zbl 1418.35349) Full Text: DOI arXiv Euclid
Cavalcanti, Marcelo M.; Domingos Cavalcanti, Valéria N.; Fukuoka, Ryuichi; Pampu, Ademir B.; Astudillo, María Uniform decay rate estimates for the semilinear wave equation in inhomogeneous medium with locally distributed nonlinear damping. (English) Zbl 1397.35025 Nonlinearity 31, No. 9, 4031-4064 (2018). MSC: 35B40 74J30 93D15 35R01 35L71 PDFBibTeX XMLCite \textit{M. M. Cavalcanti} et al., Nonlinearity 31, No. 9, 4031--4064 (2018; Zbl 1397.35025) Full Text: DOI
Beauchard, Karine; Laurent, Camille Local exact controllability of the \(2D\)-Schrödinger-Poisson system. (English. French summary) Zbl 1375.35419 J. Éc. Polytech., Math. 4, 287-336 (2017). MSC: 35Q40 35Q41 93C10 93C20 PDFBibTeX XMLCite \textit{K. Beauchard} and \textit{C. Laurent}, J. Éc. Polytech., Math. 4, 287--336 (2017; Zbl 1375.35419) Full Text: DOI
Dehman, Belhassen; Ervedoza, Sylvain Observability estimates for the wave equation with rough coefficients. (Estimées d’observabilité pour l’équation des ondes avec des coefficients continus.) (English. French summary) Zbl 1368.35046 C. R., Math., Acad. Sci. Paris 355, No. 5, 499-514 (2017). MSC: 35B45 35L05 35Q93 93B05 93C20 PDFBibTeX XMLCite \textit{B. Dehman} and \textit{S. Ervedoza}, C. R., Math., Acad. Sci. Paris 355, No. 5, 499--514 (2017; Zbl 1368.35046) Full Text: DOI
Gimperlein, Heiko; Waters, Alden A deterministic optimal design problem for the heat equation. (English) Zbl 1353.35315 SIAM J. Control Optim. 55, No. 1, 51-69 (2017). MSC: 35R30 58J35 93B07 PDFBibTeX XMLCite \textit{H. Gimperlein} and \textit{A. Waters}, SIAM J. Control Optim. 55, No. 1, 51--69 (2017; Zbl 1353.35315) Full Text: DOI arXiv
Tebou, Louis Stabilization of some elastodynamic systems with localized Kelvin-Voigt damping. (English) Zbl 1350.93072 Discrete Contin. Dyn. Syst. 36, No. 12, 7117-7136 (2016). MSC: 93D15 74J05 35L05 74H40 PDFBibTeX XMLCite \textit{L. Tebou}, Discrete Contin. Dyn. Syst. 36, No. 12, 7117--7136 (2016; Zbl 1350.93072) Full Text: DOI
Burq, Nicolas; Joly, Romain Exponential decay for the damped wave equation in unbounded domains. (English) Zbl 1351.35168 Commun. Contemp. Math. 18, No. 6, Article ID 1650012, 27 p. (2016). MSC: 35Q53 93D15 93B05 35B41 35B45 PDFBibTeX XMLCite \textit{N. Burq} and \textit{R. Joly}, Commun. Contemp. Math. 18, No. 6, Article ID 1650012, 27 p. (2016; Zbl 1351.35168) Full Text: DOI arXiv
Fernández-Cara, Enrique; Lü, Qi; Zuazua, Enrique Null controllability of linear heat and wave equations with nonlocal spatial terms. (English) Zbl 1346.93071 SIAM J. Control Optim. 54, No. 4, 2009-2019 (2016). MSC: 93B05 93B07 PDFBibTeX XMLCite \textit{E. Fernández-Cara} et al., SIAM J. Control Optim. 54, No. 4, 2009--2019 (2016; Zbl 1346.93071) Full Text: DOI
Acosta, Sebastian A control approach to recover the wave speed (conformal factor) from one measurement. (English) Zbl 1334.35414 Inverse Probl. Imaging 9, No. 2, 301-315 (2015). MSC: 35R30 35L05 35Q93 PDFBibTeX XMLCite \textit{S. Acosta}, Inverse Probl. Imaging 9, No. 2, 301--315 (2015; Zbl 1334.35414) Full Text: DOI arXiv
Marica, Aurora; Zuazua, Enrique Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach. (English) Zbl 1375.81163 Found. Comput. Math. 15, No. 6, 1571-1636 (2015). Reviewer: Charis Harley (Johannesburg) MSC: 81S30 35A21 37C05 65M06 70K05 81T80 PDFBibTeX XMLCite \textit{A. Marica} and \textit{E. Zuazua}, Found. Comput. Math. 15, No. 6, 1571--1636 (2015; Zbl 1375.81163) Full Text: DOI Link
Fanelli, Francesco; Zuazua, Enrique Weak observability estimates for 1-D wave equations with rough coefficients. (English. French summary) Zbl 1320.93027 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 2, 245-277 (2015). MSC: 93B07 35L05 35Q93 PDFBibTeX XMLCite \textit{F. Fanelli} and \textit{E. Zuazua}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 2, 245--277 (2015; Zbl 1320.93027) Full Text: DOI arXiv
Tebou, Louis Simultaneous controllability of some uncoupled semilinear wave equations. (English) Zbl 1307.93189 Discrete Contin. Dyn. Syst. 35, No. 8, 3721-3743 (2015). MSC: 93C20 35K51 35L53 35L71 93B05 93B07 PDFBibTeX XMLCite \textit{L. Tebou}, Discrete Contin. Dyn. Syst. 35, No. 8, 3721--3743 (2015; Zbl 1307.93189) Full Text: DOI
Lazar, Martin; Zuazua, Enrique Averaged control and observation of parameter-depending wave equations. (Contrôle et observation en moyenne d’équations des ondes dépendant de paramètres.) (English. French summary) Zbl 1302.35043 C. R., Math., Acad. Sci. Paris 352, No. 6, 497-502 (2014). MSC: 35B30 35L05 35R30 35A27 93B07 PDFBibTeX XMLCite \textit{M. Lazar} and \textit{E. Zuazua}, C. R., Math., Acad. Sci. Paris 352, No. 6, 497--502 (2014; Zbl 1302.35043) Full Text: DOI Link
Alabau-Boussouira, Fatiha Insensitizing exact controls for the scalar wave equation and exact controllability of 2-coupled cascade systems of PDE’s by a single control. (English) Zbl 1291.93032 Math. Control Signals Syst. 26, No. 1, 1-46 (2014). MSC: 93B05 35L05 93C20 PDFBibTeX XMLCite \textit{F. Alabau-Boussouira}, Math. Control Signals Syst. 26, No. 1, 1--46 (2014; Zbl 1291.93032) Full Text: DOI arXiv
Dehman, Belhassen; Le Rousseau, Jérôme; Léautaud, Matthieu Controllability of two coupled wave equations on a compact manifold. (English) Zbl 1290.35278 Arch. Ration. Mech. Anal. 211, No. 1, 113-187 (2014). Reviewer: Yuanyuan Ke (Beijing) MSC: 35Q93 93B05 35L05 93B07 47F05 PDFBibTeX XMLCite \textit{B. Dehman} et al., Arch. Ration. Mech. Anal. 211, No. 1, 113--187 (2014; Zbl 1290.35278) Full Text: DOI HAL
Alabau-Boussouira, Fatiha; Léautaud, Matthieu Indirect controllability of locally coupled wave-type systems and applications. (English) Zbl 1293.35167 J. Math. Pures Appl. (9) 99, No. 5, 544-576 (2013). Reviewer: Vyacheslav I. Maksimov (Ekaterinburg) MSC: 35L51 35L90 35Q93 93B05 93B07 93C05 93C20 PDFBibTeX XMLCite \textit{F. Alabau-Boussouira} and \textit{M. Léautaud}, J. Math. Pures Appl. (9) 99, No. 5, 544--576 (2013; Zbl 1293.35167) Full Text: DOI
Alabau-Boussouira, Fatiha Controllability of cascade coupled systems of multi-dimensional evolution PDEs by a reduced number of controls. (English. Abridged French version) Zbl 1401.93031 C. R., Math., Acad. Sci. Paris 350, No. 11-12, 577-582 (2012). MSC: 93B05 35Q93 93C20 PDFBibTeX XMLCite \textit{F. Alabau-Boussouira}, C. R., Math., Acad. Sci. Paris 350, No. 11--12, 577--582 (2012; Zbl 1401.93031) Full Text: DOI arXiv
Tebou, Louis Simultaneous observability and stabilization of some uncoupled wave equations. (English. Abridged French version) Zbl 1251.93041 C. R., Math., Acad. Sci. Paris 350, No. 1-2, 57-62 (2012). MSC: 93B07 93C20 35L05 93D21 PDFBibTeX XMLCite \textit{L. Tebou}, C. R., Math., Acad. Sci. Paris 350, No. 1--2, 57--62 (2012; Zbl 1251.93041) Full Text: DOI
Daoulatli, M. Behaviors of the energy of solutions of the wave equation with damping and external force. (English) Zbl 1234.35289 J. Math. Anal. Appl. 389, No. 1, 205-225 (2012). MSC: 35R01 35L05 35B40 PDFBibTeX XMLCite \textit{M. Daoulatli}, J. Math. Anal. Appl. 389, No. 1, 205--225 (2012; Zbl 1234.35289) Full Text: DOI
Alabau-Boussouira, Fatiha; Ammari, Kaïs Sharp energy estimates for nonlinearly locally damped PDEs via observability for the associated undamped system. (English) Zbl 1217.93034 J. Funct. Anal. 260, No. 8, 2424-2450 (2011). MSC: 93B07 93D21 93C20 35L20 PDFBibTeX XMLCite \textit{F. Alabau-Boussouira} and \textit{K. Ammari}, J. Funct. Anal. 260, No. 8, 2424--2450 (2011; Zbl 1217.93034) Full Text: DOI
Beauchard, Karine Local controllability and non-controllability for a 1D wave equation with bilinear control. (English) Zbl 1221.35221 J. Differ. Equations 250, No. 4, 2064-2098 (2011). Reviewer: Gheorghe Aniculăesei (Iaşi) MSC: 35L20 35L05 93B05 PDFBibTeX XMLCite \textit{K. Beauchard}, J. Differ. Equations 250, No. 4, 2064--2098 (2011; Zbl 1221.35221) Full Text: DOI
Li, Hongheng; Lü, Qi; Zhang, Xu Recent progress on controllability/observability for systems governed by partial differential equations. (English) Zbl 1201.93022 J. Syst. Sci. Complex. 23, No. 3, 527-545 (2010). MSC: 93B05 93C20 93B07 93C25 93B18 PDFBibTeX XMLCite \textit{H. Li} et al., J. Syst. Sci. Complex. 23, No. 3, 527--545 (2010; Zbl 1201.93022) Full Text: DOI
Alabau-Boussouira, Fatiha New trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems. (English) Zbl 1201.35042 J. Differ. Equations 249, No. 5, 1145-1178 (2010). Reviewer: Vyacheslav I. Maksimov (Ekaterinburg) MSC: 35B40 35B35 35L90 93D15 93D20 74H45 35B45 PDFBibTeX XMLCite \textit{F. Alabau-Boussouira}, J. Differ. Equations 249, No. 5, 1145--1178 (2010; Zbl 1201.35042) Full Text: DOI
Alabau-Boussouira, Fatiha A unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi-discretized vibrating damped systems. (English) Zbl 1397.35068 J. Differ. Equations 248, No. 6, 1473-1517 (2010). MSC: 35G20 34A33 34D20 35B40 35L70 70J50 74H45 93D20 PDFBibTeX XMLCite \textit{F. Alabau-Boussouira}, J. Differ. Equations 248, No. 6, 1473--1517 (2010; Zbl 1397.35068) Full Text: DOI
Alabau-Boussouira, Fatiha; Ammari, Kaïs Nonlinear stabilization of abstract systems via a linear observability inequality and application to vibrating PDE’s. (English. Abridged French version) Zbl 1185.93117 C. R., Math., Acad. Sci. Paris 348, No. 3-4, 165-170 (2010). MSC: 93D21 93C20 35L20 PDFBibTeX XMLCite \textit{F. Alabau-Boussouira} and \textit{K. Ammari}, C. R., Math., Acad. Sci. Paris 348, No. 3--4, 165--170 (2010; Zbl 1185.93117) Full Text: DOI
Guo, Lina; Wang, Zhiqiang Exact boundary observability for nonautonomous quasilinear wave equations. (English) Zbl 1197.35175 J. Math. Anal. Appl. 364, No. 1, 41-50 (2010). Reviewer: Gisèle M. Mophou (Pointe-à-Pitre) MSC: 35L72 93B07 35L20 PDFBibTeX XMLCite \textit{L. Guo} and \textit{Z. Wang}, J. Math. Anal. Appl. 364, No. 1, 41--50 (2010; Zbl 1197.35175) Full Text: DOI arXiv
Ignat, Liviu I.; Zuazua, Enrique Convergence of a two-grid algorithm for the control of the wave equation. (English) Zbl 1159.93006 J. Eur. Math. Soc. (JEMS) 11, No. 2, 351-391 (2009). MSC: 93B07 93C20 35B37 35L20 PDFBibTeX XMLCite \textit{L. I. Ignat} and \textit{E. Zuazua}, J. Eur. Math. Soc. (JEMS) 11, No. 2, 351--391 (2009; Zbl 1159.93006) Full Text: DOI Link
Zhang, Xu; Zuazua, Enrique Long-time behavior of a coupled heat-wave system arising in fluid-structure interaction. (English) Zbl 1178.74075 Arch. Ration. Mech. Anal. 184, No. 1, 49-120 (2007). Reviewer: Peter A. Velmisov (Ul’yanovsk) MSC: 74H40 74F10 74F05 35Q74 35Q79 80A20 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{E. Zuazua}, Arch. Ration. Mech. Anal. 184, No. 1, 49--120 (2007; Zbl 1178.74075) Full Text: DOI
Burq, N.; Gérard, P.; Tzvetkov, N. On nonlinear Schrödinger equations in exterior domains. (English) Zbl 1061.35126 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 21, No. 3, 295-318 (2004). MSC: 35Q55 37K05 37L50 81Q20 PDFBibTeX XMLCite \textit{N. Burq} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 21, No. 3, 295--318 (2004; Zbl 1061.35126) Full Text: DOI Numdam Numdam EuDML
Liu, K.; Yamamoto, M.; Zhang, X. Observability inequalities by internal observation and their applications. (English) Zbl 1087.93031 J. Optimization Theory Appl. 116, No. 3, 621-645 (2003). Reviewer: Hector O. Fattorini (Los Angeles) MSC: 93C20 93B05 93B07 PDFBibTeX XMLCite \textit{K. Liu} et al., J. Optim. Theory Appl. 116, No. 3, 621--645 (2003; Zbl 1087.93031) Full Text: DOI
Burq, Nicolas; Schlenker, Jean-Marc Exact controlability for the wave equation in corner domains. (Contrôle de l’équation des ondes dans des ouverts comportant des coins.) (French) Zbl 0937.35097 Bull. Soc. Math. Fr. 126, No. 4, 601-637 (1998). Reviewer: C.Popa (Iaşi) MSC: 35L20 93B05 74J20 35L05 PDFBibTeX XMLCite \textit{N. Burq} and \textit{J.-M. Schlenker}, Bull. Soc. Math. Fr. 126, No. 4, 601--637 (1998; Zbl 0937.35097) Full Text: DOI Numdam EuDML Link