Dispersive and Strichartz Estimates for Hyperbolic Equations With Constant Coefficients
Dispersive and Strichartz Estimates for Hyperbolic Equations With Constant Coefficients
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具有常数系数的双曲方程的色散和 Strichartz 估计
DOI：
10.2969/msjmemoirs/022010000
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发表时间：
2007
期刊：
影响因子：
3.8
通讯作者：
James Smith
中科院分区：
文献类型：
--
作者：
Michael Ruzhansky;James Smith
考虑了一般常系数严格双曲型偏微分方程解的色散估计和Chihartz估计。讨论了传播子的Lp − Lq范数的全局时间衰减估计，并证明了时间衰减率如何依赖于问题的几何形状。频率空间被分成几个区域，每个区域给出一定的衰减率。几何条件的特性负责特定的衰变进行了研究。从而对具有一般形式的低阶项的高阶严格双曲型方程进行了全面的分析。结果适用于福克-普朗克方程和半线性双曲方程的时间衰减估计。
Dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients are considered. The global time decay estimates of L p − L q norms of propagators is discussed, and it is shown how the time decay rates depend on the geometry of the problem. The frequency space is separated in several zones each giving a certain decay rate. Geometric conditions on characteristics responsible for the particular decay are investigated. Thus, a comprehensive analysis is carried out for strictly hyperbolic equations of high orders with lower order terms of a general form. Results are applied to time decay estimates for the Fokker–Planck equation and for semilinear hyperbolic equations.