Decay estimates for Beam equations with potential in dimension three

IF 1.7 2区 数学 Q1 MATHEMATICS
Miao Chen , Ping Li , Avy Soffer , Xiaohua Yao
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引用次数: 0

Abstract

This paper is devoted to studying time decay estimates of the solution for Beam equation (higher order type wave equation) with a potentialutt+(Δ2+V)u=0,u(0,x)=f(x),ut(0,x)=g(x) in dimension three, where V is a real-valued and decaying potential. Assume that zero is a regular point of H=Δ2+V, we first prove the following optimal time decay estimates of the solution operatorscos(tH)Pac(H)L1L|t|32andsin(tH)HPac(H)L1L|t|12. Moreover, if zero is a resonance of H, then time decay of the solution operators also is considered. It is noted that a first-kind resonance does not affect the decay rates of the propagator operators cos(tH) and sin(tH)H, but their decay will be significantly changed for the second and third-kind resonances.

三维势能束方程的衰减估计值
本文致力于研究三维中具有势utt+(Δ2+V)u=0,u(0,x)=f(x),ut(0,x)=g(x)的梁方程(高阶型波方程)解的时间衰减估计,其中 V 为实值衰减势。假设零点是 H=Δ2+V 的正则点,我们首先证明以下解算子的最优时间衰减估计值‖cos(tH)Pac(H)‖L1→∞≲|t|-32 和‖sin(tH)HPac(H)‖L1→∞≲|t|-12。此外,如果零点是 H 的共振,则还要考虑解算子的时间衰减。我们注意到,第一类共振不会影响传播算子 cos(tH) 和 sin(tH)H 的衰减率,但它们的衰减在第二类和第三类共振时会发生显著变化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.20
自引率
5.90%
发文量
271
审稿时长
7.5 months
期刊介绍: The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis
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