Decay property for a plate equation with memory-type dissipation

Yongqin Liu, Shuichi Kawashima

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

In this paper we focus on the initial value problem of the semilinear plate equation with memory in multi-dimensions (n > 1), the decay structure of which is of regularity-loss property. By using Fourier transform and Laplace transform, we obtain the fundamental solutions and thus the solution to the corresponding linear problem. Appealing to the point-wise estimate in the Fourier space of solutions to the linear problem, we get estimates and properties of solution operators, by exploiting which decay estimates of solutions to the linear problem are obtained. Also by introducing a set of time-weighted Sobolev spaces and using 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.

Original languageEnglish
Pages (from-to)531-547
Number of pages17
JournalKinetic and Related Models
Volume4
Issue number2
DOIs
Publication statusPublished - Jun 1 2011

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Plate Equation
Sobolev spaces
Initial value problems
Laplace transforms
Dissipation
Fourier transforms
Decay
Data storage equipment
Decay Estimates
Multi-dimension
Contraction Mapping
Pointwise Estimates
Weighted Sobolev Spaces
Semilinear Equations
Fundamental Solution
Semilinear
Laplace transform
Initial Value Problem
Fourier transform
Regularity

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation

Cite this

Decay property for a plate equation with memory-type dissipation. / Liu, Yongqin; Kawashima, Shuichi.

In: Kinetic and Related Models, Vol. 4, No. 2, 01.06.2011, p. 531-547.

Research output: Contribution to journalArticle

Liu, Yongqin ; Kawashima, Shuichi. / Decay property for a plate equation with memory-type dissipation. In: Kinetic and Related Models. 2011 ; Vol. 4, No. 2. pp. 531-547.
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