Chinese Quarterly Journal of Mathematics ›› 2013, Vol. 28 ›› Issue (4): 485-491.

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Energy Decay of Solution to a Nonlinear Wave Equation of Kirchhoff Type

  

  • Received:2011-10-10 Online:2013-12-30 Published:2023-02-16
  • About author:SONG Zhi-hua(1975-), male, native of Xinxiang, Henan, a lecturer of North China University of Water Resources and Electric Power, M.S.D., engages in nonlinear hyperbolic equation.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11271336)

Abstract: The paper studies the asymptotic behavior of solution to the initial boundary value problem for a nonlinear hyperbolic equation of Kirchhoff type utt-M(∥A 1/2 u∥2)Au + ut-|u|au = 0: It proves the global existence of solution by constructing a stable set and the energy exponential decay estimate by applying a lemma of V Komorn

Key words: wave equation of Kirchho? type, initial boundary value problem, exponential decay estimate

CLC Number: