Institute of Mathematics

References:
[1] M. Aassila, M. M. Cavalcanti, J. A. Soriano: Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain. SIAM J. Control Optim. 38 (2000), 1581-1602. DOI 10.1137/S0363012998344981 | MR 1766431 | Zbl 0985.35008
[2] Z. Achouri, N. E. Amroun, A. Benaissa: The Euler-Bernoulli beam equation with boundary dissipation of fractional derivative type. Math. Methods Appl. Sci. 40 (2017), 3837-3854. DOI 10.1002/mma.4267 | MR 3668815 | Zbl 1366.93484
[3] S. Aizicovici, E. Feireisl: Long-time stabilization of solutions to a phase-field model with memory. J. Evol. Equ. 1 (2001), 69-84. DOI 10.1007/PL00001365 | MR 1838321 | Zbl 0973.35037
[4] M. M. Cavalcanti, H. P. Oquendo: Frictional versus viscoelastic damping in a semilinear wave equation. SIAM J. Control Optimization 42 (2003), 1310-1324. DOI 10.1137/S0363012902408010 | MR 2044797 | Zbl 1053.35101
[5] R. Chill, E. Fašangová: Convergence to steady states of solutions of semilinear evolutionary integral equations. Calc. Var. Partial Differ. Equ. 22 (2005), 321-342. DOI 10.1007/s00526-004-0278-5 | MR 2118902 | Zbl 1087.45005
[6] B. D. Coleman, E. H. Dill: On the thermodynamics of electromagnetic fields in materials with memory. Arch. Rational Mech. Anal. 41 (1971), 132-162. DOI 10.1007/BF00281371 | MR 0347245
[7] B. D. Coleman, E. H. Dill: Thermodynamic restriction on the constitutive equations of electromagnetic theory. Zeit. Angew. Math. Phys. 22 (1971), 691-702. DOI 10.1007/BF01587765 | Zbl 0218.35072
[8] C. M. Dafermos: Asymptotic stability in viscoelasticity. Arch. Ration. Mech. Anal. 37 (1970), 297-308. DOI 10.1007/BF00251609 | MR 0281400 | Zbl 0214.24503
[9] W. Desch, E. Fašangová, J. Milota, G. Propst: Stabilization through viscoelastic boundary damping: a semigroup approach. Semigroup Forum 80 (2010), 405-415. DOI 10.1007/s00233-009-9197-2 | MR 2647481 | Zbl 1193.35149
[10] A. C. Eringen, G. A. Maugin: Electrodynamics of Continua. I. Foundations and Solid Media. Springer, New York (1990). DOI 10.1007/978-1-4612-3226-1 | MR 1031714
[11] M. Fabrizio, A. Morro: Thermodynamics of electromagnetic isothermal system with memory. J. Non-Equilibrium Thermodyn. 22 (1997), 110-128. DOI 10.1515/jnet.1997.22.2.110 | Zbl 0889.73004
[12] C. Giorgi, M. G. Naso, V. Pata: Energy decay of electromagnetic systems with memory. Math. Models Methods Appl. Sci. 15 (2005), 1489-1502. DOI 10.1142/S0218202505000844 | MR 2168942 | Zbl 1078.35018
[13] X. Han, M. Wang: Global existence and uniform decay for a nonlinear viscoelastic equation with damping. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70 (2009), 3090-3098. DOI 10.1016/j.na.2008.04.011 | MR 2503053 | Zbl 1173.35579
[14] X. Han, M. Wang: General decay of energy for a viscoelastic equation with nonlinear damping. Math. Methods Appl. Sci. 33 (2010), 346-358. DOI 10.1002/mma.1041 | MR 2484178 | Zbl 1161.35319
[15] V. Komornik, E. Zuazua: A direct method for the boundary stabilization of the wave equation. J. Math. Pures Appl. (9) 69 (1990), 33-54. MR 1054123 | Zbl 0636.93064
[16] J.-L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Etudes mathematiques. Dunod; Gauthier-Villars, Paris, 1969. (In French.) MR 0259693 | Zbl 0189.40603
[17] M. Matignon, J. Audounet, G. Montseny: Energy decay rate for wave equations with damping of fractional order. Fourth Int. Conf. Mathematical and Numerical Aspects of Wave Propagation Phenomena (1998), 638-640.
[18] L. P. V. Matos, V. Dmitriev: On the stability of energy and harmonic waves in conductors with memory. SBMO/IEEE MTT-S Int. Microwave and Optoelectronics Conf. (IMOC) IEEE, Belem (2009), 528-532. DOI 10.1109/IMOC.2009.5427530
[19] G. A. Maugin: Continuum Mechanics of Electromagnetic Solids. North-Holland Series in Applied Mathematics and Mechanics 33. North-Holland, Amsterdam (1988). DOI 10.1002/zamm.19890691106 | MR 0954611 | Zbl 0652.73002
[20] B. Mbodje: Wave energy decay under fractional derivative controls. IMA J. Math. Control Inf. 23 (2006), 237-257. DOI 10.1093/imamci/dni056 | MR 2211512 | Zbl 1095.93015
[21] S. A. Messaoudi: General decay of the solution energy in a viscoelastic equation with a nonlinear source. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69 (2008), 2589-2598. DOI 10.1016/j.na.2007.08.035 | MR 2446355 | Zbl 1154.35066
[22] J. E. Muñoz Rivera, M. G. Naso, E. Vuk: Asymptotic behaviour of the energy for electromagnetic systems with memory. Math. Methods Appl. Sci. 27 (2004), 819-841. DOI 10.1002/mma.473 | MR 2055321 | Zbl 1054.35103
[23] S. Nicaise, C. Pignotti: Stabilization of the wave equation with variable coefficients and boundary condition of memory type. Asymptotic Anal. 50 (2006), 31-67. MR 2286936 | Zbl 1139.35373
[24] J. Y. Park, S. H. Park: Decay rate estimates for wave equations of memory type with acoustic boundary conditions. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74 (2011), 993-998. DOI 10.1016/j.na.2010.09.057 | MR 2738648 | Zbl 1202.35032
[25] V. Pata, A. Zucchi: Attractors for a damped hyperbolic equation with linear memory. Adv. Math. Sci. Appl. 11 (2001), 505-529. MR 1907454 | Zbl 0999.35014
[26] S.-T. Wu: General decay and blow-up of solutions for a viscoelastic equation with nonlinear boundary damping-source interactions. Z. Angew. Math. Phys. 63 (2012), 65-106. DOI 10.1007/s00033-011-0151-2 | MR 2878734 | Zbl 1242.35053
[27] H. Yassine: Stability of global bounded solutions to a nonautonomous nonlinear second order integro-differential equation. Z. Anal. Anwend. 37 (2018), 83-99. DOI 10.4171/ZAA/1604 | MR 3746499 | Zbl 06852543
[28] R. Zacher: Convergence to equilibrium for second order differential equations with weak damping of memory type. Adv. Differ. Equ. 14 (2009), 749-770. MR 2527692 | Zbl 1190.45007