Open Access
Volume 25, 2019
Article Number 33
Number of page(s) 38
Published online 09 September 2019
  1. F. Ali Mehmeti, A characterisation of generalized c notion on nets. Integr. Equ. Oper. Theory 9 (1986) 753–766. [CrossRef] [Google Scholar]
  2. F. Ali Mehmeti, Nonlinear Wave in Networks. Vol. 80 of Math. Res. Akademie Verlag (1994). [Google Scholar]
  3. K. Ammari and S. Nicaise, Stabilization of Elastic Systems by Collocated Feedback. Vol. 2124 of Lecture Notes in Mathematics. Springer, Cham (2015). [CrossRef] [Google Scholar]
  4. C. Amrouche, C. Bernardi, M. Dauge and V. Girault, Vector potentials in three-dimensional non-smooth domains. Math. Methods Appl. Sci. 21 (1998) 823–864. [Google Scholar]
  5. H. Arfaoui, F. Ben Belgacem, H. El Fekih and J.-P. Raymond, Boundary stabilizability of the linearized viscous Saint-Venant system. Discrete Contin. Dyn. Syst. Ser. B 15 (2011) 491–511. [Google Scholar]
  6. G. Bastin and J.-M. Coron, Stability and Boundary Stabilization of 1-D Hyperbolic Systems. PNLDE Subseries in Control. Birkhäuser, Basel (2016). [CrossRef] [Google Scholar]
  7. G. Bastin, J.-M. Coron and B. d’Andréa Novel, On Lyapunov stability of linearised Saint-Venant equations for a sloping channel. Netw. Heterog. Media 4 (2009) 177–187. [CrossRef] [Google Scholar]
  8. J. von Below, A characteristic equation associated to an eigenvalue problem on c2-networks. Linear Algebra Appl. 71 (1985) 309–325. [Google Scholar]
  9. J. von Below, Classical solvability of linear parabolic equations on networks. J. Differ. Equ. 72 (1988) 316–337. [Google Scholar]
  10. J. von Below, Sturm-Liouville eigenvalue problems on networks. Math. Methods Appl. Sci. 10 (1988) 383–395. [Google Scholar]
  11. G. Berkolaiko and P. Kuchment, Introduction to Quantum Graphs. Vol. 186 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2013). [Google Scholar]
  12. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011). [Google Scholar]
  13. S. Chowdhury, M. Ramaswamy and J.-P. Raymond, Controllability and stabilizability of the linearized compressible Navier-Stokes system in one dimension. SIAM J. Control Optim. 50 (2012) 2959–2987. [Google Scholar]
  14. J.-M. Coron, Control and Nonlinearity. Vol. 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2007). [Google Scholar]
  15. S. Cox and E. Zuazua, The rate at which energy decays in a damped string. Commun. Partial Differ. Equ. 19 (1994) 213–243. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Dáger and E. Zuazua, Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures. Vol. 50 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer-Verlag, Berlin (2006). [Google Scholar]
  17. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. In Vol. 3 of Spectral theory and applications, With the collaboration of Michel Artola and Michel Cessenat, Translated from the French by John C. Amson. Springer-Verlag, Berlin (1990). [Google Scholar]
  18. C. De Coster and S. Nicaise, Introduction à quelques problèmes d’EDP. Notes du groupe de travail de l’équipe EDP du Laboratoire de Mathématiques et leurs Applications de Valenciennes. Editions universitaires européennes (2014). [Google Scholar]
  19. J. de Halleux, C. Prieur, J.-M. Coron, B. d’Andréa Novel and G. Bastin, Boundary feedback control in networks of open channels. Autom. J. IFAC 39 (2003) 1365–1376. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.-M. Dominguez, Etude des équations de la magnéto-hydrodynamique stationnaire et de leur approximation par éléments finis. Thèse de 3eme cycle, Université Pierre et Marie Curie (1982). [Google Scholar]
  21. D. Dutykh and F. Dias, Viscous potential free-surface flows in a fluid layer of finite depth. C. R. Math. Acad. Sci. Paris 345 (2007) 113–118. [CrossRef] [Google Scholar]
  22. G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Travaux et Recherches Mathématiques, No. 21, Dunod, Paris (1972). [Google Scholar]
  23. S. Evje and K.H. Karlsen, Global existence of weak solutions for a viscous two-phase model. J. Differ. Equ. 245 (2008) 2660–2703. [Google Scholar]
  24. C. Foiaş and R. Temam, Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 (1978) 28–63. [Google Scholar]
  25. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms. Vol. 5 of Springer Series in Computational Mathematics. Springer, Berlin (1986). [CrossRef] [Google Scholar]
  26. D. Hoff and K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow. Indiana Univ. Math. J. 44 (1995) 603–676. [CrossRef] [Google Scholar]
  27. F.L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces. Ann. Differ. Equ. 1 (1985) 43–56. [Google Scholar]
  28. V. Komornik, Boundary stabilization, observation and control of Maxwell’s equations. PanAm. Math. J. 4 (1994) 47–61. [Google Scholar]
  29. J.E. Lagnese, G. Leugering and E. Schmidt, Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures. Birkhäuser, Boston (1994). [CrossRef] [Google Scholar]
  30. H.V.J. Le Meur, Derivation of a viscous Boussinesq system for surface water waves. Asymptot. Anal. 94 (2015) 309–345. [CrossRef] [Google Scholar]
  31. G. Leugering and E.J.P.G. Schmidt, On the modelling and stabilization of flows in networks of open canals. SIAM J. Control Optim. 41 (2002) 164–180. [Google Scholar]
  32. G. Lumer, Connecting of local operators and evolution equations on networks, in Potential Theory, Copenhagen 1979 (Proc. Colloq., Copenhagen, 1979). Vol. 787 of Lecture Notes in Math. Springer, Berlin (1980) 219–234. [CrossRef] [Google Scholar]
  33. P. Monk, Finite element methods for Maxwell’s equations. Numerical Analysis and Scientific Computation Series Oxford Univ. Press, New York (2003). [Google Scholar]
  34. P.B. Mucha and W.M. Zajaczkowski, On a Lp-estimate for the linearized compressible Navier-Stokes equations with the Dirichlet boundary conditions. J. Differ. Equ. 186 (2002) 377–393. [Google Scholar]
  35. S. Nicaise, Spectre des réseaux topologiques finis. Bull. Sc. Math., 2ème série 111 (1987) 401–413. [Google Scholar]
  36. S. Nicaise, Exact boundary controllability of Maxwell’s equations in heterogeneous media and an application to an inverse source problem. SIAM J. Control Optim. 38 (2000) 1145–1170. [Google Scholar]
  37. V. Perrollaz and L. Rosier, Finite-time stabilization of 2 × 2 hyperbolic systems on tree-shaped networks. SIAM J. Control Optim. 52 (2014) 143–163. [Google Scholar]
  38. K.D. Phung, Contrôle et stabilisation d’ondes électromagnétiques. ESAIM: COCV 5 (2000) 87–137. [CrossRef] [EDP Sciences] [Google Scholar]
  39. C. Pignotti, Observability and controllability of Maxwell’s equations. Rend. Mat. Appl. 19 (1999) 523–546. [Google Scholar]
  40. J. Prüss, On the spectrum of C0-semigroups. Trans. Amer. Math. Soc. 284 (1984) 847–857. [Google Scholar]
  41. G. Ströhmer, About the resolvent of an operator from fluid dynamics. Math. Z. 194 (1987) 183–191. [CrossRef] [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.