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Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary

김대욱
영남수학회 (Youngnam Mathematical Society)|2018.01|East Asian Mathematical Journal|제34권 제1호|pp. 69-84|DOI http://dx.doi.org/10.7858/eamj.2018.008

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참고문헌

키워드

viscoelastic Kirchhoff type equationindependent kernelsenergy decay rateenergy functionalsmallness condition.
주제분류수학

초록

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

Abstract

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

참고문헌 (18)

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  15. 김대욱, "STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE", East Asian Mathematical Journal, 32(1), pp.117~128 (2016), 영남수학회[DOI]
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  17. 김대욱, "EXPONENTIAL STABILITY FOR THE GENERALIZED KIRCHHOFF TYPE EQUATION IN THE PRESENCE OF PAST AND FINITE HISTORY", East Asian Mathematical Journal, 32(5), pp.659~675 (2016), 영남수학회[DOI]
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