TY - JOUR

T1 - Decay property for a plate equation with memory-type dissipation

AU - Liu, Yongqin

AU - Kawashima, Shuichi

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/6

Y1 - 2011/6

N2 - 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.

AB - 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.

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U2 - 10.3934/krm.2011.4.531

DO - 10.3934/krm.2011.4.531

M3 - Article

AN - SCOPUS:79957943709

SN - 1937-5093

VL - 4

SP - 531

EP - 547

JO - Kinetic and Related Models

JF - Kinetic and Related Models

IS - 2

ER -