Asymptotic profiles for damped plate equations with rotational inertia terms

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED Journal of Hyperbolic Differential Equations Pub Date : 2019-05-10 DOI:10.1142/s0219891620500162

Tomonori Fukushima, R. Ikehata, Hironori Michihisa

引用次数: 4

Abstract

We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We derive asymptotic profiles of the solution in [Formula: see text]-sense as [Formula: see text] in the case when the initial data have high and low regularity, respectively. Especially, in the low regularity case of the initial data one encounters the regularity-loss structure of the solutions, and the analysis is more delicate. We employ the so-called Fourier splitting method combined with the explicit formula of the solution (high-frequency estimates) and the method due to [R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Differential Equations 257 (2014) 2159–2177.] (low-frequency estimates). In this paper, we will introduce a new threshold [Formula: see text] on the regularity of the initial data that divides the property of the corresponding solution to our problem into two parts: one is wave-like, and the other is parabolic-like.

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含转动惯量项的阻尼板方程的渐近轮廓

我们考虑了具有转动惯量和摩擦阻尼项的板方程的Cauchy问题。在初始数据分别具有高正则性和低正则性的情况下，我们导出了[公式：见文本]意义上的解的渐近轮廓。特别是，在初始数据的低正则性情况下，人们会遇到解的正则性损失结构，并且分析更加精细。我们采用了所谓的傅立叶分裂方法，结合了解的显式公式（高频估计）和[R.Ikehata的方法，强阻尼波动方程的渐近剖面，J.Differential equations 257（2014）2159–2177.]（低频估计）。在本文中，我们将引入一个关于初始数据正则性的新阈值[公式：见正文]，该阈值将我们问题的相应解的性质划分为两部分：一部分是波浪形的，另一部分是抛物线形的。

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.

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