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http://dx.doi.org/10.4134/BKMS.2006.43.2.245

ENERGY DECAY ESTIMATES FOR A KIRCHHOFF MODEL WITH VISCOSITY  

Jung Il-Hyo (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
Choi Jong-Sool (KOREA SCIENCE ACADEMY)
Publication Information
Bulletin of the Korean Mathematical Society / v.43, no.2, 2006 , pp. 245-252 More about this Journal
Abstract
In this paper we study the uniform decay estimates of the energy for the nonlinear wave equation of Kirchhoff type $$y with the damping constant ${\delta} > 0$ in a bounded domain ${\Omega}\;{\subset}\;\mathbb{R}^n$.
Keywords
stabilization; quasilinear hyperbolic equation; Kirchhoff equation; asymptotic behavior; energy decay;
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Times Cited By SCOPUS : 2
연도 인용수 순위
1 G. Chen, Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures Appl. 58 (1979), no. 3, 249-273
2 G. Chen and D. L. Russell, A mathematical model for linear elastic systems with structural damping, Quart. Appl. Math. 39 (1982), no. 4, 433-454   DOI
3 Julio G. Dix, Decay of solutions of a degenerate hyperbolic equation, Electron. J. Differential Equations 1998 (1998), no. 21, 1-10
4 G. C. Gorain, Exponential energy decay estimate for the solutions of internally damped wave equation in a bounded domain, J. Math. Anal. Appl. 216 (1997), no. 2, 510-520   DOI   ScienceOn
5 I. H. Jung and Y. H. Lee, Exponential Decay for the solutions of wave equation of Kirchhoff type with strong damping, Acta Math. Hungar. 92 (2001), no. 1-2, 163-170   DOI
6 V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation, J. Math. Pures Appl. (9) 69 (1990), no. 1, 33-54
7 I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping, Differential Integral Equations 6 (1993), no. 3, 507-533
8 J. Y. Park, I. H. Jung, and Y. H. Kang, Generalized quasilinear hyperbolic equa- tions and Yosida approximations, J. Aust. Math. Soc. 74 (2003), no. 1, 69-86   DOI
9 J. Y. Park and I. H. Jung, On a class of quasilinear hyperbolic equations and Yosida approximations, Indian J. Pure Appl. Math. 30 (1999), no. 11, 1091- 1106
10 J. E. Lions, On some questions in boundary value problems of mathematical physics : in International Symposium on Continuum Mechanics and Partial Dif- ferential Equations, Rio de Janeiro, 1977, Noth-Holland, Amsterdam, 1978
11 M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. S. Prates Filho and J. A. Soriano, Existence and exponential decay for a Kirchhoff-Carrier model with vis- cosity, J. Math. Anal. Appl. 226 (1998), no. 1, 40-60   DOI   ScienceOn
12 G. Kirchhoff, Vorlesungen uber Mechanik, Teubner, Leipzig, 1883
13 R. M. Christensen, Theory of Viscoelasticity, Academic Press, New York, 1971
14 J. Quinn and D. L. Russel, Asymptotic stability and energy decay for solutions of hyperbolic equations with boundary damping, Proc. Roy. Soc. Edinburgh. Sect. A 77 (1977), 97-127
15 Y. Yamada, On some quasilinear wave equations with dissipative terms, Nagoya Math. J. 87 (1982), 17-39   DOI
16 E. Zuazua, Stability and decay for a class of nonlinear hyperbolic problems, As- ymptotic Anal. 1 (1988), no. 2, 161-185