Acta mathematica scientia, Series B >
GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION
Received date: 2013-08-26
Revised date: 2013-11-13
Online published: 2014-09-20
Supported by
This research was supported by Basic Science Re-search Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (20110007870).
In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.
Sun Hye PARK . GENERAL DECAY OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION[J]. Acta mathematica scientia, Series B, 2014 , 34(5) : 1395 -1403 . DOI: 10.1016/S0252-9602(14)60091-6
[1] Andrade D, Fatori L H. The nonlinear transmission problem with memory. Bol Soc Parana Mat, 2004, 22(3): 106–118
[2] Andrade D, Fatori L H, Munoz Rivera J E. Nonlinear transmission problem with a dissipative boundary condition of memory type. Electron J Differential Equations, 2006, 2006(53): 1–16
[3] Bae J J. Nonlinear trasmission problem for wave equation with boundary condition of memory type. Acta Appl Math, 2010, 110: 907–919
[4] Cavalcanti M M, Guesmia A. General decay rates of solutions to a nonlinear wave equation with boundary conditions of memory type. Differential Integral Equations, 2005, 18: 583–600
[5] Dautray R, Lions J L. Analyse Math´ematique et Calcul Num´erique pour les Sciences et les Techniques, Vol 1. Paris: Masson, 1984
[6] Guesmia A, Messaoudi S.A. General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping. Math Methods Appl Sci, 2009, 32: 2102–2122
[7] Ladyzhenskaya O A, Ural’tseva N N. Linear and Quasilinear Elliptic Equations. New York: Academic Press, 1968
[8] Ma T F, Munoz Rivera J E. Positive solutins for a nonlinear nonlocal elliptic transmission problem. Appl Math Lett, 2003, 16: 243–248
[9] Messaoudi S A. General decay of solutions of a viscoelastic equation. J Math Anal Appl, 2008, 341: 1457–1467
[10] Messaoudi S A, Said-Houari B. Energy decay in a transmission problem in thermoelasticity of type III. IMA J Appl Math, 2009, 74: 344–360
[11] Messaoudi S A, Soufyane A. General decay of solutions of a wave equation with a boundary control of memory type. Nonlinear Anal: RWA, 2010, 11: 2896–2904
[12] Munoz Rivera J E, Oquendo H P. The transmission problem of viscoelastic waves. Acta Appl Math, 2000, 62: 1–21
[13] Park J Y, Park S H. Decay rate estimates for wave equations of memory type with acoustic boundary conditions. Nonlinear Anal: TMA, 2011, 74: 993–998
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