|
[1]
|
G. S. Aragão and F. D. M. Bezerra, Upper semicontinuity of the pullback attractors of non-autonomous damped wave equations with terms concentrating on the boundary, J. Math. Anal. Appl., 462 (2018), 871-899.
doi: 10.1016/j.jmaa.2017.12.047.
|
|
[2]
|
G. S. Aragão and S. M. Bruschi, Concentrated terms and varying domains in elliptic equations: Lipschitz case, Math. Methods Appl. Sci., 39 (2016), 3450-3460.
doi: 10.1002/mma.3791.
|
|
[3]
|
G. S. Aragão, A. L. Pereira and M. Pereira, Attractors for a nonlinear parabolic problem with terms concentrating on the boundary, J. Dynam. Differential Equations, 26 (2014), 871-888.
doi: 10.1007/s10884-014-9412-z.
|
|
[4]
|
G. S. Aragão and S. M. Oliva, Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary, J. Differential Equations, 253 (2012), 2573-2592.
doi: 10.1016/j.jde.2012.07.008.
|
|
[5]
|
G. S. Aragão, A. L. Pereira and M. Pereira, A nonlinear elliptic problem with terms concentrating in the boundary, Math. Methods Appl. Sci., 35 (2012), 1110-1116.
doi: 10.1002/mma.2525.
|
|
[6]
|
J. M. Arrieta, A. Jiménez-Casas and A. Rodríguez-Bernal, Nonhomogeneous flux condition as lim of concentrated reactions, Revista Iberoamericana de Matematicas, 24 (2008), 183-211.
|
|
[7]
|
J. M. Arrieta, A. Rodríguez–Bernal and J. Rossi, The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary, Proceedings of The Royal Society of Edinburgh, 138A (2008), 223-237.
doi: 10.1017/S0308210506000813.
|
|
[8]
|
J. M. Ball, Strongly continuous semigroups, weak solutions and the variation of constants formula, Proc. American Math. Soc., 63 (1977), 370-373.
doi: 10.2307/2041821.
|
|
[9]
|
C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation control and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), 1024 -1065.
doi: 10.1137/0330055.
|
|
[10]
|
G. A. Chechkin, D. Cioranescu, A. Damlamian and A. L. Piatnitski, On boundary value problem with singular inhomogeneity concentrated on the boundary, J. Math. Pures Appl., 98 (2012), 115-138.
doi: 10.1016/j.matpur.2011.11.002.
|
|
[11]
|
P. Cornilleau, J. P. Loheác and A. Osses, Nonlinear Neumann boundary stabilization of the wave equation using rotated multipliers, J. of Dynamical and Control Systems, 16 (2010), 163-188.
doi: 10.1007/s10883-010-9088-6.
|
|
[12]
|
Y. D. Golovaty, D. Gómez, M. Lobo and E. Pérez, On vibrating membranes with very heavy thin inclusions, Math. Models Methods Appl. Sci., 14 (2004), 987-1034.
doi: 10.1142/S0218202504003520.
|
|
[13]
|
D. Gómez, M. Lobo, S. A. Nazarov and E. Pérez, Spectral stiff problems in domains surrounded by thin bands: asymptotic and uniform estimates for eigenvalues, J. Math. Pures Appl., 85 (2006), 598-632.
doi: 10.1016/j.matpur.2005.10.013.
|
|
[14]
|
Á. Jiménez-Casas and A. Rodríguez-Bernal, Singular limit for a nonlinear parabolic equation with terms concentrating on the boundary, J. Math. Anal. and Appl., 379 (2011), 567-588.
doi: 10.1016/j.jmaa.2011.01.051.
|
|
[15]
|
A. Jiménez-Casas and A. Rodríguez-Bernal, Dynamic boundary conditions as a singular limit of parabolic problems with terms concentrating at the boundary, Dynamics of Partial Differential Equations, 9 (2012), 341-368.
doi: 10.4310/DPDE.2012.v9.n4.a3.
|
|
[16]
|
V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl., 69 (1990), 33-54.
|
|
[17]
|
J. Lagnese, Note on the boundary stabilization of wave equations, SIAM J. Control Optim., 26 (1988), 1250-1256.
doi: 10.1137/0326068.
|
|
[18]
|
J. Lagnese, Boundary Stabilization of Thin Plates, SIAM Studies in Appl. Math., vol. 10, 1989.
doi: 10.1137/1.9781611970821.
|
|
[19]
|
P. D. Lamberti, Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems, Complex Var. Elliptic Equ., 59 (2014), 309-323.
doi: 10.1080/17476933.2011.557155.
|
|
[20]
|
I. Lasiecka and R. Triggiani, Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Cambridge University Press, 2000.
|
|
[21]
|
J. L. Lions, Quelques Méthodes de Rèsolution des Problèmes aux Limes non Lineaires, Dunod, 1969.
|
|
[22]
|
J. L. Lions, Contrôlabilité Exacte, Stabilisation et Perturbations de Systèmes Distribués. Tome 1. Contrôlabilité Exacte, Masson, Paris, RMA 8, 1988.
|
|
[23]
|
J. L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., 30 (1988), 1-68.
doi: 10.1137/1030001.
|
|
[24]
|
M. Nakao, Stabilization of local energy in an exterior domain for the wave equation with a localized dissipation, J. of Differential Equations, 148 (1998), 388-406.
doi: 10.1006/jdeq.1998.3468.
|
|
[25]
|
O. A. Oleinik, J. Sanchez-Hubert and G. A. Yosifian, On the vibration of membranes with concentrated masses, Bull. Sci. Math., 15 (1991), 1-27.
|
|
[26]
|
M. C. Pereira, Remarks on semilinear parabolic systems with terms concentrating in the boundary, Nonlinear Analysis: Real World Applications, 14 (2013), 1921-1930.
doi: 10.1016/j.nonrwa.2013.01.003.
|
|
[27]
|
A. Rodríguez-Bernal, A singular perturbation in a linear parabolic equation with terms concentrating on the boundary, Revista Matemática Complutense, 25 (2012), 165-197.
doi: 10.1007/s13163-011-0064-9.
|
|
[28]
|
A. Rodríguez-Bernal and E. Zuazua, Parabolic singular lim of a wave equation with localized boundary damping, Dis. Cont. Dyn. Sys., 1 (1995), 303-346.
doi: 10.3934/dcds.1995.1.303.
|
|
[29]
|
A. Rodríguez-Bernal and E. Zuazua, Parabolic singular limit of a wave equation with localized interior damping, Comm. Contemp. Math., 3 (2001), 215-257.
doi: 10.1142/S0219199701000330.
|
|
[30]
|
D. L. Russell, Controllability and stabilizability theory for linear partial differential equa- tions. Recent progress and open questions, SIAM Rev., 20 (1978), 639-739.
doi: 10.1137/1020095.
|
|
[31]
|
E. Zuazua, Exponential decay for the semilinear wave equation with locally distributed damping, Comm. Partial Differential Equations, 15 (1990), 205-235.
doi: 10.1080/03605309908820684.
|
{{journal.titleEn}} 
Download:
