Decay Estimates of Solutions to the Semi-Linear Plate Equation with Memory

doi:10.3969/j.cnki.jdxb.2017.03.003

Journal of Jishou University（Natural Sciences Edition)

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Decay Estimates of Solutions to the Semi-Linear Plate Equation with Memory

WU Xuehui,LIU Yongqin

(Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

Online:2017-05-25 Published:2017-06-19

Abstract

Abstract:

The initial value problem of the semi-linear plate equation with memory in multi-dimension Rⁿ(n≥1) is studied.In the Fourier space,we obtain the decay estimates of solutions to the linear problem.And through introducing a set of time-weighted Sobolev spaces and applying the contraction mapping theorem,we obtain the global in-time existence and the optimal decay estimates of solutions to the semi-linear problem under smallness assumption on the initial data.

Key words: plate equation, memory, decay estimates, regularity-loss type

WU Xuehui,LIU Yongqin. Decay Estimates of Solutions to the Semi-Linear Plate Equation with Memory[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.3969/j.cnki.jdxb.2017.03.003.

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Decay Estimates of Solutions to the Semi-Linear Plate Equation with Memory

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