有限时间尺度内川原方程小数据解的分散衰减约束

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-05-24 DOI:10.1007/s00028-024-00980-9

Jongwon Lee

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引用次数: 0

摘要

在这篇文章中，我们证明了小局部数据产生的川原式方程解在有限时间尺度上具有线性色散衰减，这取决于初始数据的大小。我们使用与 Ifrim 和 Tataru 类似的方法来推导 KdV 方程解的色散衰减约束，但某些步骤更为简单。这一结果有望成为具有二次非线性的五阶分散方程小数据全局约束的第一个结果。

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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Dispersive decay bound of small data solutions to Kawahara equation in a finite time scale

In this article, we prove that small localized data yield solutions to Kawahara-type equations which have linear dispersive decay on a finite time scale depending on the size of the initial data. We use the similar method used by Ifrim and Tataru to derive the dispersive decay bound of the solutions to the KdV equation, with some steps being simpler. This result is expected to be the first result of the small data global bounds of the fifth-order dispersive equations with quadratic nonlinearity.

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators