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http://dx.doi.org/10.4134/CKMS.2009.24.1.085

HYPERBOLIC HEMIVARIATIONAL INEQUALITIES WITH BOUNDARY SOURCE AND DAMPING TERMS  

Jeong, Jin-Mun (DIVISION OF MATHEMATICAL SCIENCES PUKYONG NATIONAL UNIVERSITY)
Park, Jong-Yeoul (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
Park, Sun-Hye (BASIC SCIENCES RESEARCH INSTITUTE PUKYONG NATIONAL UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.24, no.1, 2009 , pp. 85-97 More about this Journal
Abstract
In this paper we study the existence of global weak solutions for a hyperbolic hemivariational inequalities with boundary source and damping terms, and then investigate the asymptotic stability of the solutions by using Nakao Lemma [8].
Keywords
hemivariational inequality; existence of solution; asymptotic stability; source term;
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1 P. D. Panagiotopoulos, Modelling of nonconvex nonsmooth energy problems. Dynamic hemivariational inequalities with impact effects, J. Comput. Appl. Math. 63 (1995), 123-138.   DOI   ScienceOn
2 M. Miettinen and P. D. Panagiotopoulos, On parabolic hemivariational inequalities and applications, Nonlinear Anal. 35 (1999), 885-915.   DOI   ScienceOn
3 M. Nakao, A difference inequality and its application to nonlinear evolution equations, J. Math. Soc. Japan 30 (1978), 747-762.   DOI
4 S. A. Messaoudi, Global existence and nonexistence in a system of Petrovsky, J. Math. Anal. Appl. 265 (2002), 296-308.   DOI   ScienceOn
5 M. Miettinen, A parabolic hemivariational inequality, Nonlinear Anal. 26 (1996), 725-734.   DOI   ScienceOn
6 S. Carl and S. Heikkila, Existence results for nonlocal and nonsmooth hemivariational inequalities, Journal of Inequalities and Applications 2006 (2006), Article ID 79532, 13 pages.   DOI   ScienceOn
7 J. L. Lions, Quelques methodes de resolution des problemes aux limites non linéaires, Dunod-Gauthier Villars, Paris, 1969.
8 G. Todorova, Stable and unstable sets for the Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms, J. Math. Anal. Appl. 239 (1999), 213-226.   DOI   ScienceOn
9 C. Varga, Existence and infinitely many solutions for an abstract class of hemivariational inequlaities, Journal of Inequalities and Applications 2005 (2005), 89-105.   DOI   ScienceOn
10 R. Adams, Sobolev Spaces, Academic Press, New York, 1975.
11 M. Nakao, Energy decay for the quasilinear wave equation with viscosity, Math. Z. 219 (1995), 289-299.   DOI
12 R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Mathematical Surveys and Monographs, 49, American Mathematical Society, Providence, RI, 1996.
13 J. Rauch, Discontinuous semilinear differential equations and multiple valued maps, Proc. Amer. Math. Soc. 64 (1977), 277-282.   DOI
14 J. Y. Park and S. H. Park, On solutions for a hyperbolic system with differential inclusion and memory source term on the boundary, Nonlinear Anal. 57 (2004), 459-472.   DOI   ScienceOn
15 L. Liu and M. Wang, Global existence and blow-up of solutions for some hyperbolic systems with damping and source terms, Nonlinear Analysis 64 (2006), 69-91.   DOI   ScienceOn
16 J. Y. Park and J. J. Bae, On the existence of solutions of the degenerate wave equations with nonlinear damping terms, J. Korean Math. Soc. 35 (1998), 465-489.   과학기술학회마을
17 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.   DOI   ScienceOn
18 P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applicatons. Convex and Nonconvex Energy Functions, Birkhäuser, Basel, Boston, 1985.
19 K. Ono, On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation, J. Math. Anal. Appl. 216 (1997), 321-342.   DOI   ScienceOn