East Asian mathematical journal

  • 제32권3호
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  • Pages.399-412
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  • 2016
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM

  • Kim, Daewook (Department of Mathematics and Education Seowon University)
  • 투고 : 2016.04.19
  • 심사 : 2016.05.13
  • 발행 : 2016.05.31
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초록

In this paper, we study the viscoelastic Kirchhoff type equation with the following nonlinear source and time-varying delay $$u_{tt}-M(x,t,{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\int_{0}^{t}}h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\+{\parallel}u{\parallel}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ 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.

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참고문헌

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피인용 문헌

  1. Global existence of solutions to a viscoelastic non-degenerate Kirchhoff equation pp.1563-504X, 2020, https://doi.org/10.1080/00036811.2018.1544621
  2. EXPONENTIAL STABILITY FOR THE GENERALIZED KIRCHHOFF TYPE EQUATION IN THE PRESENCE OF PAST AND FINITE HISTORY vol.32, pp.5, 2016, https://doi.org/10.7858/eamj.2016.046
  3. Global Existence and Decay of Solutions for a Class of Viscoelastic Kirchhoff Equation vol.43, pp.1, 2020, https://doi.org/10.1007/s40840-018-00708-2
  4. Global Existence and Decay of Solutions for Coupled Nondegenerate Kirchhoff System with a Time Varying Delay Term vol.2020, pp.None, 2020, https://doi.org/10.1155/2020/6324971
  5. Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms vol.2020, pp.None, 2016, https://doi.org/10.1155/2020/7105387
  6. Asymptotic Behavior for a Viscoelastic Kirchhoff-Type Equation with Delay and Source Terms vol.171, pp.1, 2016, https://doi.org/10.1007/s10440-021-00387-5