Abstract
We prove the existence and uniform decay rates of global solutions for a hyperbolic system with a discontinuous and nonlinear multi-valued term and a nonlinear memory source term on the boundary.
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References
M. Aassila: Global existence of solutions to a wave equation with damping and source terms. Diff. Int. Eqs. 14 (2001), 1301–1314.
M. M. Cavalcanti: Existence and uniform decay for the Euler-Bernoulli viscoelastic equation with nonlocal boundary dissipation. Discrete Contin. Dynam. Systems 8 (2002), 675–695.
M. M. Cavalcanti, V. N. Domingos Cavalcanti, T. F. Ma and J. A. Soriano: Global existence and asymptotic stability for viscoelastic problems. Diff. Int. Eqs. 15 (2002), 731–748.
L. Gasiński: Existence of solutions for hyperbolic hemivariational inequalities. J. Math. Anal. Appl. 276 (2002), 723–746.
L. Gasiński and N. S. Papageorgiou: Nonlinear hemivariational inequalities at resonance. J. Math. Anal. Appl. 244 (2000), 200–213.
V. Kormornik and E. Zuazua: A direct method for the boundary stabilization of the wave equation. J. Math. Pures et Appl. 69 (1990), 33–54.
J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non liné aires. Dunod-Gauthier Villars, Paris, 1969.
M. Miettinen: A parabolic hemivariational inequality. Nonlinear Anal. 26 (1996), 725–734.
M. Miettinen and P. D. Panagiotopoulos: On parabolic hemivariational inequalities and applications. Nonlinear Anal. 35 (1999), 885–915.
J. E. Munoz Rivera and A. P. Salvatierra: Asymptotic behavior of the energy in partially viscoelastic materials. Quart. Appl. Math. 59 (2001), 557–578.
P. D. Panagiotopoulos: Inequality Problems in Mechanics and Applincations. Convex and Nonconvex Energy Functions, Birkhäuser, Basel, Boston, 1985.
P. D. Panagiotopoulos,: Hemivariational Inequalities and Applications in Mechanics and Engineering. Springer, New York, 1993.
J. Y. Park and J. J. Bae: On coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term. Appl. Math. Comput. 129 (2002), 87–105.
J. Y. Park, H. M. Kim and S. H. Park: On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities. Nonlinear Anal. 55 (2003), 103–113.
J. Rauch: Discontinuous semilinear differential equations and multiple valued maps. Proc. Amer. Math. Soc. 64 (1977), 277–282.
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Park, J.Y., Park, S.H. Uniform decay for a hyperbolic system with differential inclusion and nonlinear memory source term on the boundary. Czech Math J 59, 287–303 (2009). https://doi.org/10.1007/s10587-009-0021-7
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DOI: https://doi.org/10.1007/s10587-009-0021-7