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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2016.1
- 수록면
- 659 - 675 (17page)
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In this paper, we study the generalized Kirchhoff type equation in the presence of past and finite history\begin{eqnarray*}&& u_{tt}-M(x,t,\tau, \|\nabla u(t)\|^2)\Delta u+\int_0^t h(t-\tau) div [a(x)\nabla u(\tau)]d\tau\\&&\qquad -\int_{-\infty}^{t} k(t-\tau)\Delta u(x,t) d\tau+|u|^\gamma u + \mu_1 u_t(x,t)+\mu_2 u_t(x,t-s(t))=0.
\end{eqnarray*}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.
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참고문헌 (18)
참고문헌 신청
김대욱 / 2016 / ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM / East Asian Mathematical Journal 32(3):399~412
S. Nicaise / 2011 / Interior feedback stabilization of wave equations with time dependent delay / Electron. J. Differential Equations 41:1~20
W. Liu / 2013 / General decay rate estimate for the energy of a weak viscoelastic equation with an internal time-varying delay term / Taiwanese journal of mathematics 17:2101~2115
김대욱 / 2016 / STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE / East Asian Mathematical Journal 32(1):117~128
F. Li / 2011 / Global existence and uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation / J Nonlinear Analysis:Real World Applications 12:1759~1773
S. Nicaise / 2011 / Interior feedback stabilization of wave equations with time dependent delay / Electron. J. Differential Equations 41:1~20
W. Liu / 2013 / General decay rate estimate for the energy of a weak viscoelastic equation with an internal time-varying delay term / Taiwanese journal of mathematics 17:2101~2115
김대욱 / 2016 / STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE / East Asian Mathematical Journal 32(1):117~128
F. Li / 2011 / Global existence and uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation / J Nonlinear Analysis:Real World Applications 12:1759~1773
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