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EXPONENTIAL STABILITY FOR THE GENERALIZED KIRCHHOFF TYPE EQUATION IN THE PRESENCE OF PAST AND FINITE HISTORY

김대욱
영남수학회 (Youngnam Mathematical Society)|2016.09|East Asian Mathematical Journal|제32권 제5호|pp. 659-675|DOI http://dx.doi.org/10.7858/eamj.2016.046

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참고문헌

키워드

energy decay rateenergy functionalsmallness conditiongeneralized Kirchhoff type equationthe presence of past and finite historyinternal time-varying delay
주제분류수학

초록

In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history utt-M(x,t,τ,‖▽u(t)‖2)△u+∫t-h(t-τ)div[a(x)▽u(τ)]dτ-∫t-∞k(t-τ)△u(x,t)dτ+|u|γu+μ1ut(x,t)+μ2ut(x,t+s(t))=0. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.

Abstract

In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history utt-M(x,t,τ,‖▽u(t)‖2)△u+∫t-h(t-τ)div[a(x)▽u(τ)]dτ-∫t-∞k(t-τ)△u(x,t)dτ+|u|γu+μ1ut(x,t)+μ2ut(x,t+s(t))=0. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the expoential decay rate of the Kirchhoff type energy.

참고문헌 (18)

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ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제1호Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary김대욱영남수학회 · East Asian Mathematical Journal2018 · 제34권 제1호Energy decay for a viscoelastic equation with Balakrishnan-Taylor damping involving infinite memory and nonlinear time-varying delay terms in dynamical boundaryAbita Rahmoune, Soufiane Benkouider대한수학회 · 대한수학회논문집2023 · 제38권 제3호On solvability of the dissipative Kirchhoff equation with nonlinear boundary dampingJian-Hua Huang, Zai-Yun Zhang대한수학회 · 대한수학회보2014 · 제51권 제1호GENERAL DECAY OF SOLUTIONS OF NONLINEAR VISCOELASTIC WAVE EQUATION강수진, 신기연영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호

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