THE OPTIMAL LARGE TIME BEHAVIOR OF 3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR DAMPING

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外文摘要：We are concerned with the large-time behavior of 3D quasilinear hyperbolic e-quations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L2 convergence rate of the k(e[0,3])-order spatial derivatives of the solution is(1+t)-3+2k/4.Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

外文关键词：

quasilinear hyperbolic equationslarge time behavioroptimal decay rates

作者：

王涵、张映辉

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作者单位：

School of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China

基金：

National Nature Science Foundation of ChinaGuangxi Natural Science FoundationGuangxi Natural Science FoundationGuangxi Natural Science FoundationInnovation Project of Guangxi Graduate EducationKey Laboratory of Mathematical Model and Application(Guangxi Normal University)Education Department of Guangxi Zhuang Autonomous Region

项目编号：

122711142023JJD1100092019JJG1100032019AC20214JGY2023061

出版年：

2024

DOI：

10.1007/s10473-024-0317-6

数学物理学报(英文版)

中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD

影响因子：0.256

ISSN：0252-9602

年,卷(期)：2024.44(3)