Estimates for a class of oscillatory integrals and decay rates for wave-type equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:394

Article

Arnold, Anton¹  Kim, JinMyong^1,2  Yao, Xiaohua³ 

[1] Tech Univ Wien, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[2] Kim II Sung Univ, Dept Math, Pyongyang, North Korea

[3] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China

关键词: Oscillatory integral;    Higher-order wave equation;    Fundamental solution estimate;   

DOI  :  10.1016/j.jmaa.2012.04.070

来源: Elsevier

【 摘 要 】

This paper investigates higher order wave-type equations of the form partial derivative(u)u + P(D-x)u = 0, where the symbol P(xi) is a real, non-degenerate elliptic polynomial of the order m >= 4 on R-n. Using methods from harmonic analysis, we first establish global pointwise time-space estimates for a class of oscillatory integrals that appear as the fundamental solutions to the Cauchy problem of such wave equations. These estimates are then used to establish (pointwise-in-time) L-p-L-q estimates on the wave solution M terms of the initial conditions. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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