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Exponential decay for solutions to semilinear damped wave equation
Some singular perturbations results for semilinear hyperbolic problems
1. | University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zurich |
2. | Department of Mathematics, University of M’sila, BP:166, 28000, M’sila, Algeria |
References:
[1] |
B. Brighi and S. Guesmia, Asymptotic behaviour of solutions of hyperbolic problems on a cylindrical domain, in "Discrete Contin. Dyn. Syst.," 2007, Dynamical Systems and Differential Equations, Proceedings of the 6th AIMS International Conference, suppl., 160-169. |
[2] |
M. Chipot, On some anisotropic singular perturbation problems, Asymptot. Ana., 55 (2007), 125-144. |
[3] |
M. Chipot and S. Guesmia, On the asymptotic behavior of elliptic, anisotropic singular perturbations problems, Commun. Pure Appl. Anal., 8 (2009), 179-193. |
[4] |
M. Chipot and S. Guesmia, On a class of integro-differential problems, Commun. Pure Appl. Anal., 9 (2010), 1249-1262.
doi: 10.3934/cpaa.2010.9.1249. |
[5] |
M. Chipot and S. Guesmia, On some anisotropic, nonlocal, parabolic singular perturbations problems, Applicable Analysis, to appear. |
[6] |
M. Chipot and S. Guesmia, Correctors for some asymptotic problems, Proc. Steklov Inst. Math., 270 (2010), 263-277.
doi: 10.1134/S0081543810030211. |
[7] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions, Discrete Contin. Dyn. Syst. Ser. B, 1 (2001), 319-338.
doi: 10.3934/dcdsb.2001.1.319. |
[8] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Math. Acad. Sci. Paris, 346 (2008), 21-26. |
[9] |
S. Guesmia, "Etude du Comportement Asymptotique de certaines Équations aux Dérivées Partielles dans des Domaines Cylindriques," Thèse Université de Haute Alsace, 2006. |
[10] |
S. Guesmia, Some results on the asymptotic behavior for hyperbolic problems in cylindrical domains becoming unbounded, J. Math. Anal. Appl., 341 (2008), 1190-1212.
doi: 10.1016/j.jmaa.2007.11.001. |
[11] |
S. Guesmia, Asymptotic behaviour of elliptic boundary-value problems with some small coefficients, Electron. J. Differential Equations, 59 (2008), 1-13. |
[12] |
S. Guesmia and A. Sengouga, Anisotropic singular perturbation of hyperbolic problems, Appl. Math. Comput. 217 (2011), 8983-8996.
doi: 10.1016/j.amc.2011.03.104. |
[13] |
J.-L. Lions, "Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal," Lecture Notes in Math., 323, Springer-Verlag, Berlin-New York, 1973. |
[14] |
J.-L. Lions and W. A. Strauss, Some non-linear evolution equations, Bull. Soc. Math. France, 93 (1965), 43-96. |
[15] |
W. A. Strauss, On continuity of functions with values in various Banach spaces, Pacific J. Math., 19 (1966), 543-551. |
show all references
References:
[1] |
B. Brighi and S. Guesmia, Asymptotic behaviour of solutions of hyperbolic problems on a cylindrical domain, in "Discrete Contin. Dyn. Syst.," 2007, Dynamical Systems and Differential Equations, Proceedings of the 6th AIMS International Conference, suppl., 160-169. |
[2] |
M. Chipot, On some anisotropic singular perturbation problems, Asymptot. Ana., 55 (2007), 125-144. |
[3] |
M. Chipot and S. Guesmia, On the asymptotic behavior of elliptic, anisotropic singular perturbations problems, Commun. Pure Appl. Anal., 8 (2009), 179-193. |
[4] |
M. Chipot and S. Guesmia, On a class of integro-differential problems, Commun. Pure Appl. Anal., 9 (2010), 1249-1262.
doi: 10.3934/cpaa.2010.9.1249. |
[5] |
M. Chipot and S. Guesmia, On some anisotropic, nonlocal, parabolic singular perturbations problems, Applicable Analysis, to appear. |
[6] |
M. Chipot and S. Guesmia, Correctors for some asymptotic problems, Proc. Steklov Inst. Math., 270 (2010), 263-277.
doi: 10.1134/S0081543810030211. |
[7] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions, Discrete Contin. Dyn. Syst. Ser. B, 1 (2001), 319-338.
doi: 10.3934/dcdsb.2001.1.319. |
[8] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Math. Acad. Sci. Paris, 346 (2008), 21-26. |
[9] |
S. Guesmia, "Etude du Comportement Asymptotique de certaines Équations aux Dérivées Partielles dans des Domaines Cylindriques," Thèse Université de Haute Alsace, 2006. |
[10] |
S. Guesmia, Some results on the asymptotic behavior for hyperbolic problems in cylindrical domains becoming unbounded, J. Math. Anal. Appl., 341 (2008), 1190-1212.
doi: 10.1016/j.jmaa.2007.11.001. |
[11] |
S. Guesmia, Asymptotic behaviour of elliptic boundary-value problems with some small coefficients, Electron. J. Differential Equations, 59 (2008), 1-13. |
[12] |
S. Guesmia and A. Sengouga, Anisotropic singular perturbation of hyperbolic problems, Appl. Math. Comput. 217 (2011), 8983-8996.
doi: 10.1016/j.amc.2011.03.104. |
[13] |
J.-L. Lions, "Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal," Lecture Notes in Math., 323, Springer-Verlag, Berlin-New York, 1973. |
[14] |
J.-L. Lions and W. A. Strauss, Some non-linear evolution equations, Bull. Soc. Math. France, 93 (1965), 43-96. |
[15] |
W. A. Strauss, On continuity of functions with values in various Banach spaces, Pacific J. Math., 19 (1966), 543-551. |
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