المؤلفون: Beilina, Larisa, Ruas, Vitoriano

مصطلحات موضوعية: keyword:constant magnetic permeability, keyword:dielectric permittivity, keyword:explicit scheme, keyword:finite element, keyword:mass lumping, keyword:Maxwell-wave equation, msc:65M12, msc:65M22, msc:65M60

وصف الملف: application/pdf

العلاقة: mr:MR4541076; zbl:Zbl 07655740; reference:[1] Ammari, H., Hamdache, K.: Global existence and regularity of solutions to a system of nonlinear Maxwell equations.J. Math. Anal. Appl. 286 (2003), 51-63. Zbl 1039.35122, MR 2009617, 10.1016/S0022-247X(03)00415-3; reference:[2] Asadzadeh, M., Beilina, L.: On stabilized $P_1$ finite element approximation for time harmonic Maxwell's equations.Available at https://arxiv.org/abs/1906.02089v1Test (2019), 25 pages. MR 4141133; reference:[3] Asadzadeh, M., Beilina, L.: Convergence of stabilized $P_1$ finite element scheme for time harmonic Maxwell's equations.Mathematical and Numerical Approaches for Multi-Wave Inverse Problems Springer Proceedings in Mathematics and Statistics 328. Springer, Cham (2020), 33-43. Zbl 1446.65158, MR 4141133, 10.1007/978-3-030-48634-1_4; reference:[4] Assous, F., Degond, P., Heintze, E., Raviart, P. A., Segre, J.: On a finite-element method for solving the three-dimensional Maxwell equations.J. Comput. 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الإتاحة: https://doi.org/10.1006/jcph.1993.1214Test
https://doi.org/10.1515/crll.1982.337.77Test
https://doi.org/10.21136/AM.2022.0210-21Test
http://hdl.handle.net/10338.dmlcz/151497Test

المؤلفون: Luo, Yuesheng, Xing, Ruixue, Li, Xiaole

مصطلحات موضوعية: keyword:regularized long wave equation, keyword:integral method with variational limit, keyword:finite difference method, keyword:Lagrange interpolation, keyword:energy conservation scheme, msc:65M06, msc:65M12

وصف الملف: application/pdf

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الإتاحة: https://doi.org/10.21136/AM.2021.0066-20Test
http://hdl.handle.net/10338.dmlcz/149081Test

المؤلفون: Wang, Xiao-Rui, Xu, Gen-Qi

مصطلحات موضوعية: keyword:boundary control, keyword:disturbance, keyword:wave equation, keyword:anti-disturbance, msc:35B35, msc:93C05, msc:93C20

وصف الملف: application/pdf

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الإتاحة: https://doi.org/10.21136/AM.2019.0070-18Test
http://hdl.handle.net/10338.dmlcz/147929Test

المؤلفون: Esquivel-Avila, Jorge A.

مصطلحات موضوعية: keyword:Klein-Gordon equation, Blow up, High energies, Abstract wave equation, Generalized Boussinesq equation, msc:35B35, msc:35B40, msc:35L70

وصف الملف: application/pdf

العلاقة: reference:[1] Esquivel-Avila, J.: Remarks on the qualitative behavior of the undamped Klein-Gordon equation., Math. Meth. Appl. Sci. (2017) 9 pp., DOI:10.1002/mma.4598. MR 3745359, 10.1002/mma.4598; reference:[2] Esquivel-Avila, J.: Nonexistence of global solutions of abstract wave equations with high energies., J. of Inequalities and Applications, 2017:268 (2017) 14 pp., DOI 10.1186/s13660017-1546-1. MR 3716687, 10.1186/s13660-017-1546-1; reference:[3] Ball, J.: Finite blow up in nonlinear problems., in Nonlinear Evolution Equations, M. G. Crandall Editor, Academic Press, 1978, pp. 189-205. MR 0513819; reference:[4] Ball, J.: Remarks on blow up and nonexistence theorems for nonlinear evolution equations., Quart. J. Math. Oxford 28 (1977) 473-486. MR 0473484, 10.1093/qmath/28.4.473; reference:[5] Willem, M.: Minimax Theorems., Progress in Nonlinear Differential Equations and Applications, Vol. 24, Birkh\"auser, 1996. MR 1400007; reference:[6] Payne, L. E., Sattinger, D. H.: Saddle points and instability of nonlinear hyperbolic equations., Israel J. Math. 22 (1975) 273-303. MR 0402291, 10.1007/BF02761595; reference:[7] Gazzola, F., Squassina, M.: Global solutions and finite time blow up for damped semilinear wave equations., Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 185-207. MR 2201151; reference:[8] Esquivel-Avila, J.: Blow up and asymptotic behavior in a nondissipative nonlinear wave equation., Appl. Anal. 93 (2014) 1963-1978. MR 3227792, 10.1080/00036811.2013.859250; reference:[9] Wang, Y.: A sufficient condition for finite time blow up of the nonlinear Klein-Gordon equations with arbitrary positive initial energy., Proc. Amer. Math. Soc. 136 (2008) 3477-3482. MR 2415031, 10.1090/S0002-9939-08-09514-2; reference:[10] Korpusov, M. O.: Blowup of a positive-energy solution of model wave equations in nonlinear dynamics., Theoret. and Math. Phys. 171 421-434 (2012). MR 3168856, 10.1007/s11232-012-0041-6; reference:[11] Kutev, N., Kolkovska, N., Dimova, M.: Sign-preserving functionals and blow up to Klein-Gordon equation with arbitrary high energy., Appl. Anal. 95 (2016) 860-873. MR 3475853, 10.1080/00036811.2015.1038994; reference:[12] Dimova, M., Kolkovska, N., Kutev, N.: Revised concavity method and application to Klein-Gordon equation., Filomat 30 (2016) 831-839. MR 3498681, 10.2298/FIL1603831D; reference:[13] Alinhac, S.: Blow up for nonlinear hyperbolic equations., Progress in Nonlinear Differential Equations and Applications 17, Birkh\"auser, 1995. MR 1339762; reference:[14] Levine, H. A.: Instability and nonexistence of global solutions to nonlinear wave equations of the form $P u_{tt} = −Au + \Cal F (u)$. Trans. Am. Math. Soc. 192 (1974) 1-21. MR 0344697; reference:[15] Wang, S., Xuek, H.: Global solution for a generalized Boussinesq equation., Appl. Math. Comput. 204 (2008) 130-136. MR 2458348; reference:[16] Xu, R., Liu, Y.: Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations., J. Math. Anal. Appl. 359 (2009) 739-751. MR 2546791, 10.1016/j.jmaa.2009.06.034; reference:[17] Kutev, N., Kolkovska, N., Dimova, M.: Nonexistence of global solutions to new ordinary differential inequality and applications to nonlinear dispersive equations., Math. Meth. Appl. Sci.39 (2016) 2287-2297. MR 3510159, 10.1002/mma.3639; reference:[18] Kutev, N., Kolkovska, N., Dimova, M.: Finite time blow up of the solutions to Boussinesq equation with linear restoring force and arbitrary positive energy., Acta Math. Scientia 36B (2016)881-890. MR 3479262

الإتاحة: https://doi.org/10.1002/mma.4598Test
https://doi.org/10.1186/s13660017-1546-1Test.
http://hdl.handle.net/10338.dmlcz/703020Test

المؤلفون: Slavík, Jakub

مصطلحات موضوعية: keyword:Strongly damped wave equation, unbounded domains, locally compact attractor, Kolmogorovs entropy, msc:35B41, msc:35L05, msc:37L30

وصف الملف: application/pdf

العلاقة: reference:[1] Belleri, V., Pata, V.: Attractors for semilinear strongly damped wave equations on $\Bbb R^3$., Discrete Contin. Dynam. Systems, 7 (2001), pp. 719–735. MR 1849655, 10.3934/dcds.2001.7.719; reference:[2] Carvalho, A. N., Cholewa, J. W.: Attractors for strongly damped wave equations with critical nonlinearities., Pacific J. Math., 207 (2002), pp. 287–310. MR 1972247, 10.2140/pjm.2002.207.287; reference:[3] Cholewa, J. W., Dlotko, T.: Strongly damped wave equation in uniform spaces., Nonlinear Anal., 64 (2006), pp. 174–187. MR 2183836, 10.1016/j.na.2005.06.021; reference:[4] Conti, M., Pata, V., Squassina, M.: Strongly damped wave equations on $\Bbb R^3$ with critical nonlinearities., Commun. Appl. Anal., 9 (2005), pp. 161–176. MR 2168756; reference:[5] Plinio, F. Di, Pata, V., Zelik, S.: On the strongly damped wave equation with memory., Indiana Univ. Math. J., 57 (2008), pp. 757–780. MR 2414334, 10.1512/iumj.2008.57.3266; reference:[6] Ghidaglia, J.-M., Marzocchi, A.: Longtime behaviour of strongly damped wave equations, global attractors and their dimension., SIAM J. Math. Anal., 22 (1991), pp. 879–895. MR 1112054, 10.1137/0522057; reference:[7] Grasselli, M., Pražák, D., Schimperna, G.: Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories., J. Differential Equations, 249 (2010), pp. 2287–2315. MR 2718659, 10.1016/j.jde.2010.06.001; reference:[8] Kalantarov, V., Zelik, S.: Finite-dimensional attractors for the quasi-linear strongly damped wave equation., J. Differential Equations, 247 (2009), pp. 1120–1155. MR 2531174, 10.1016/j.jde.2009.04.010; reference:[9] Li, H., Zhou, S.: Kolmogorov ε-entropy of attractor for a non-autonomous strongly damped wave equation., Commun. Nonlinear Sci. Numer. Simul., 17 (2012), pp. 3579–3586. MR 2913994, 10.1016/j.cnsns.2012.01.025; reference:[10] Michálek, M., Pražák, D., HASH(0x2ff9058), Slavík, J.: Semilinear damped wave equation in locally uniform spaces., Commun. Pure Appl. Anal., 16 (2017), pp. 1673–1695. MR 3661796, 10.3934/cpaa.2017080; reference:[11] Pata, V., Squassina, M.: On the strongly damped wave equation., Comm. Math. Phys., 253 (2005), pp. 511–533. MR 2116726, 10.1007/s00220-004-1233-1; reference:[12] Pražák, D.: On finite fractal dimension of the global attractor for the wave equation with nonlinear damping., J. Dynam. Differential Equations, 14 (2002), pp. 763–776. MR 1940102, 10.1023/A:1020756426088; reference:[13] Roubíček, T.: Nonlinear partial differential equations with applications., Birkhäuser/Springer Basel AG, Basel, International Series of Numerical Mathematics 153 (2013). MR 3014456; reference:[14] Savostianov, A.: Infinite energy solutions for critical wave equation with fractional damping in unbounded domains., Nonlinear Anal., 136 (2016), pp. 136–167. MR 3474408, 10.1016/j.na.2016.02.016; reference:[15] Yang, M., Sun, C.: Dynamics of strongly damped wave equations in locally uniform spaces: attractors and asymptotic regularity., Trans. Amer. Math. Soc., 361 (2009), pp. 1069–1101. MR 2452835, 10.1090/S0002-9947-08-04680-1; reference:[16] Yang, M., Sun, C.: Exponential attractors for the strongly damped wave equations., Nonlinear Anal. Real World Appl., 11 (2010), pp. 913–919. MR 2571264, 10.1016/j.nonrwa.2009.01.022; reference:[17] Zelik, S. V.: The attractor for a nonlinear hyperbolic equation in the unbounded domain., Discrete Contin. Dynam. Systems, 7 (2001), pp. 593–641. MR 1815770, 10.3934/dcds.2001.7.593

الإتاحة: http://hdl.handle.net/10338.dmlcz/703040Test

المؤلفون: Baňas, Ľubomír, Brzeźniak, Zdzisław, Neklyudov, Mikhail, Ondreját, Martin, Prohl, Andreas

مصطلحات موضوعية: keyword:geometric stochastic wave equation, keyword:stochastic geodesic equation, keyword:ergodicity, keyword:attractivity, keyword:invariant measure, keyword:numerical approximation, msc:37A25, msc:58J65, msc:60H10, msc:60H15, msc:60H35, msc:60J60, msc:65C20, msc:65C30

وصف الملف: application/pdf

العلاقة: mr:MR3407597; zbl:Zbl 06537684; reference:[1] Aida, S., Kusuoka, S., Stroock, D.: On the support of Wiener functionals.Asymptotic Problems in Probability Theory: Wiener Functionals and Asymptotics. Proc. Conf., Sanda and Kyoto, Japan, 1990 K. D. Elworthy et al. Pitman Res. Notes Math. Ser. 284 Longman Scientific & Technical, Harlow, Essex; John Wiley & Sons, New York (1993), 3-34. Zbl 0790.60047, MR 1354161; reference:[2] Arnold, L., Kliemann, W.: On unique ergodicity for degenerate diffusions.Stochastics 21 (1987), 41-61. Zbl 0617.60076, MR 0899954, 10.1080/17442508708833450; reference:[3] Baňas, Ľ., Brzeźniak, Z., Neklyudov, M., Prohl, A.: A convergent finite-element-based discretization of the stochastic Landau-{L}ifshitz-{G}ilbert equation.IMA J. Numer. Anal. 34 (2014), 502-549. Zbl 1298.65012, MR 3194798, 10.1093/imanum/drt020; reference:[4] Baňas, Ľ., Brzeźniak, Z., Neklyudov, M., Prohl, A.: Stochastic Ferromagnetism. 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S.: On the support of diffusion processes with applications to the strong maximum principle.Proc. Conf. Berkeley, Calififornia, 1970/1971, Vol. III: Probability Theory L. M. Le Cam et al. Univ. California Press Berkeley, Calififornia (1972), 333-359. Zbl 0255.60056, MR 0400425

الإتاحة: https://doi.org/10.1007/s10587-015-0200-7Test
http://hdl.handle.net/10338.dmlcz/144435Test

المؤلفون: Tran, Minh-Binh

مصطلحات موضوعية: keyword:optimal control of the wave equation, keyword:overlapping domain decomposition methods, msc:49M25, msc:49M27, msc:49M30, msc:65M55

وصف الملف: application/pdf

العلاقة: mr:MR3204445; zbl:Zbl 1340.49029

الإتاحة: http://hdl.handle.net/10338.dmlcz/702948Test

المؤلفون: Savostianov, Anton, Zelik, Sergey

مصطلحات موضوعية: keyword:damped wave equation, keyword:fractional damping, keyword:critical nonlinearity, keyword:global attractor, keyword:smoothness, msc:35B30, msc:35B40, msc:35B41, msc:35B45, msc:35L30, msc:35L76, msc:35R11, msc:37L30

وصف الملف: application/pdf

العلاقة: mr:MR3306855; zbl:Zbl 06433689; reference:[1] Babin, A. V., Vishik, M. I.: Attractors of Evolution Equations.Studies in Mathematics and Its Applications 25 North-Holland, Amsterdam (1992), translated and revised from the 1989 Russian original. Zbl 0778.58002, MR 1156492; reference:[2] Ball, J. M.: Global attractors for damped semilinear wave equations. Partial differential equations and applications.Discrete Contin. Dyn. Syst. 10 (2004), 31-52. MR 2026182; reference:[3] Blair, M. D., Smith, H. F., Sogge, C. D.: Strichartz estimates for the wave equation on manifolds with boundary.Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009), 1817-1829. Zbl 1198.58012, MR 2566711, 10.1016/j.anihpc.2008.12.004; reference:[4] Burq, N., Lebeau, G., Planchon, F.: Global existence for energy critical waves in 3-{D} domains.J. Am. Math. Soc. 21 (2008), 831-845. Zbl 1204.35119, MR 2393429, 10.1090/S0894-0347-08-00596-1; reference:[5] Carvalho, A. N., Cholewa, J. W.: Attractors for strongly damped wave equations with critical nonlinearities.Pac. J. Math. 207 (2002), 287-310. Zbl 1060.35082, MR 1972247, 10.2140/pjm.2002.207.287; reference:[6] Carvalho, A. N., Cholewa, J. W.: Local well posedness for strongly damped wave equations with critical nonlinearities.Bull. Aust. Math. Soc. 66 (2002), 443-463. Zbl 1020.35059, MR 1939206, 10.1017/S0004972700040296; reference:[7] Carvalho, A. N., Cholewa, J. W., Dlotko, T.: Strongly damped wave problems: Bootstrapping and regularity of solutions.J. Differ. Equations 244 (2008), 2310-2333. Zbl 1151.35056, MR 2413843, 10.1016/j.jde.2008.02.011; reference:[8] Chen, S., Triggiani, R.: Gevrey class semigroups arising from elastic systems with gentle dissipation: The case $0; reference:[9] Chen, S., Triggiani, R.: Proof of extensions of two conjectures on structural damping for elastic systems.Pac. J. Math. 136 (1989), 15-55. Zbl 0633.47025, MR 0971932, 10.2140/pjm.1989.136.15; reference:[10] Chepyzhov, V. V., Vishik, M. I.: Attractors for Equations of Mathematical Physics.American Mathematical Society Colloquium Publications 49 American Mathematical Society, Providence (2002). Zbl 0986.35001, MR 1868930; reference:[11] Chueshov, I.: Global attractors for a class of Kirchhoff wave models with a structural nonlinear damping.J. Abstr. Differ. Equ. Appl. (electronic only) 1 (2010), 86-106. Zbl 1216.37026, MR 2771816; reference:[12] Chueshov, I., Lasiecka, I.: Von Karman Evolution Equations. Well-posedness and long time dynamics.Springer Monographs in Mathematics Springer, New York (2010). Zbl 1298.35001, MR 2643040; reference:[13] Feireisl, E.: Asymptotic behaviour and attractors for a semilinear damped wave equation with supercritical exponent.Proc. R. Soc. Edinb., Sect. A, Math. 125 (1995), 1051-1062. Zbl 0838.35078, MR 1361632, 10.1017/S0308210500022630; reference:[14] Grasselli, M., Schimperna, G., Segatti, A., Zelik, S.: On the 3{D} Cahn-{H}illiard equation with inertial term.J. Evol. Equ. 9 (2009), 371-404. Zbl 1239.35160, MR 2511557, 10.1007/s00028-009-0017-7; reference:[15] Grasselli, M., Schimperna, G., Zelik, S.: On the 2{D} Cahn-{H}illiard equation with inertial term.Commun. Partial Differ. Equations 34 (2009), 137-170. Zbl 1173.35086, MR 2512857, 10.1080/03605300802608247; reference:[16] Grillakis, M. G.: Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity.Ann. Math. (2) 132 (1990), 485-509. Zbl 0736.35067, MR 1078267; reference:[17] Kalantarov, V., Savostianov, A., Zelik, S.: Attractors for damped quintic wave equations in bounded domains.http://arxiv.org/abs/1309.6272Test.; reference:[18] Kalantarov, V., Zelik, S.: Finite-dimensional attractors for the quasi-linear strongly-damped wave equation.J. Differ. Equations 247 (2009), 1120-1155. Zbl 1183.35053, MR 2531174, 10.1016/j.jde.2009.04.010; reference:[19] Kapitanski, L.: Minimal compact global attractor for a damped semilinear wave equation.Commun. Partial Differ. 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الإتاحة: https://doi.org/10.21136/MB.2014.144142Test
http://hdl.handle.net/10338.dmlcz/144142Test

المؤلفون: Bradji, Abdallah, Fuhrmann, Jürgen

مصطلحات موضوعية: keyword:acoustic wave equation, keyword:finite element method, keyword:Newmark method, keyword:new error estimate, msc:35L05, msc:35L15, msc:35L20, msc:65M15, msc:65M60, msc:65N15, msc:65N30

وصف الملف: application/pdf

العلاقة: mr:MR3238828; zbl:Zbl 06362247; reference:[1] Bernardi, C., Süli, E.: Time and space adaptivity for the second-order wave equation.Math. Models Methods Appl. Sci. 15 199-225 (2005). Zbl 1070.65083, MR 2119997, 10.1142/S0218202505000339; reference:[2] Brezis, H.: Analyse Fonctionnelle: Théorie et Applications.French Collection Mathématiques Appliquées pour la Maîtrise Masson, Paris (1983). Zbl 0511.46001, MR 0697382; reference:[3] H. F. Cooper, Jr.: Propagation of one-dimensional waves in inhomogeneous elastic media.SIAM Rev. 9 671-679 (1967). Zbl 0153.56403, 10.1137/1009108; reference:[4] Dautray, R., Lions, J.-L.: Analyse Mathématique et Calcul Numérique Pour les Sciences et les Techniques.Vol. 9 French Masson, Paris (1988). Zbl 0652.45001, MR 1016606; reference:[5] Evans, L. C.: Partial Differential Equations.Graduate Studies in Mathematics 19 American Mathematical Society, Providence (1998). Zbl 0902.35002, MR 1625845; reference:[6] Feistauer, M., Felcman, J., Straškraba, I.: Mathematical and Computational Methods for Compressible Flow.Numerical Mathematics and Scientific Computation Oxford University Press, Oxford (2003). Zbl 1028.76001, MR 2261900; reference:[7] Grote, M. J., Schötzau, D.: Optimal error estimates for the fully discrete interior penalty DG method for the wave equation.J. Sci. Comput. 40 257-272 (2009). Zbl 1203.65182, MR 2511734, 10.1007/s10915-008-9247-z; reference:[8] Karaa, S.: Finite element $\theta$-schemes for the acoustic wave equation.Adv. Appl. Math. Mech. 3 181-203 (2011). Zbl 1262.65131, MR 2770084, 10.4208/aamm.10-m1018; reference:[9] Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations.Springer Series in Computational Mathematics 23 Springer, Berlin (2008). Zbl 1151.65339, MR 1299729; reference:[10] Raviart, P.-A., Thomas, J.-M.: Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles.French Collection Mathématiques Appliquées pour la Maîtrise Masson, Paris (1983). Zbl 0561.65069, MR 0773854; reference:[11] Zampieri, E., Pavarino, L. F.: Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods.J. Comput. Appl. Math. 185 (2006), 308-325. Zbl 1079.65093, MR 2169068, 10.1016/j.cam.2005.03.013

الإتاحة: https://doi.org/10.21136/MB.2014.143843Test
http://hdl.handle.net/10338.dmlcz/143843Test

المؤلفون: Park, Jong Yeoul, Park, Sun Hye

مصطلحات موضوعية: keyword:asymptotic stability, keyword:viscoelastic problems, keyword:boundary dissipation, keyword:wave equation, msc:35B35, msc:35B40, msc:35L15, msc:35L70, msc:35Q72, msc:65M60, msc:74D10, msc:74H20

وصف الملف: application/pdf

العلاقة: mr:MR2291736; zbl:Zbl 1164.35445; reference:[1] J. J. Bae, J. Y. Park, and J. M. Jeong: On uniform decay of solutions for wave equation of Kirchhoff type with nonlinear boundary damping and memory source term.Appl. Math. Comput. 138 (2003), 463–478. MR 1950077, 10.1016/S0096-3003(02)00163-7; reference:[2] E. E. Beckenbach and R. Bellman: Inequalities.Springer-Verlag, Berlin, 1971. MR 0192009; reference:[3] M. M. Cavalcanti: Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation.Discrete and Continuous Dynamical Systems 8 (2002), 675–695. Zbl 1009.74034, MR 1897875; reference:[4] M. M. Cavalcanti, V. N. Domingos Cavalcanti, T. F. Ma, and J. A. Soriano: Global existence and asymptotic stability for viscoelastic problems.Differential and Integral Equations 15 (2002), 731–748. MR 1893844; reference:[5] M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. S. Prates Filho, and J. A. Soriano: Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.Diff. Int. Eqs. 14 (2001), 85–116. MR 1797934; reference:[6] I. Lasiecka, D. Tataru: Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping.Diff. Int. Eqs. 6 (1993), 507–533. MR 1202555; reference:[7] J.-L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod-Gauthier Villars, Paris, 1969. Zbl 0189.40603, MR 0259693; reference:[8] J. Y. Park, J. J. Bae: On coupled wave equation of Kirchhoff type with nonliear boundary damping and memory term.Appl. Math. Comput. 129 (2002), 87–105. MR 1897321, 10.1016/S0096-3003(01)00031-5; reference:[9] B. Rao: Stabilization of Kirchhoff plate equation in star-shaped domain by nonlinear feedback.Nonlinear Anal., T.M.A. 20 (1993), 605–626. MR 1214731, 10.1016/0362-546X(93)90023-L; reference:[10] M. L. Santos: Decay rates for solutions of a system of wave equations with memory.Elect. J. Diff. Eqs. 38 (2002), 1–17. Zbl 1010.35012, MR 1907714; reference:[11] E. Zuazua: Uniform stabilization of the wave equation by nonlinear boundary feedback.SIAM J. Control Optim. 28 (1990), 466–477. Zbl 0695.93090, MR 1040470, 10.1137/0328025

الإتاحة: http://hdl.handle.net/10338.dmlcz/128066Test