Lower bounds on the radius of spatial analyticity for the Kawahara equation

Jaeseop Ahn; Jimyeong Kim; Ihyeok Seo

doi:10.1007/s13324-020-00447-3

Lower bounds on the radius of spatial analyticity for the Kawahara equation

Jaeseop Ahn, Jimyeong Kim, Ihyeok Seo

Department of Mathematics

Sungkyunkwan University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper we obtain lower bounds on the radius of spatial analyticity of solutions to the Kawahara equation u_t+ uu_x+ αu_xxx+ βu_xxxxx= 0 , β≠ 0 , given initial data which is analytic with a fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time t can decay no faster than 1/|t| as | t| → ∞.

Original language	English
Article number	28
Journal	Analysis and Mathematical Physics
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/s13324-020-00447-3
State	Published - Mar 2021

Keywords

Kawahara equation
Spatial analyticity

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10.1007/s13324-020-00447-3

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title = "Lower bounds on the radius of spatial analyticity for the Kawahara equation",

abstract = "In this paper we obtain lower bounds on the radius of spatial analyticity of solutions to the Kawahara equation ut+ uux+ αuxxx+ βuxxxxx= 0 , β≠ 0 , given initial data which is analytic with a fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time t can decay no faster than 1/|t| as | t| → ∞.",

keywords = "Kawahara equation, Spatial analyticity",

author = "Jaeseop Ahn and Jimyeong Kim and Ihyeok Seo",

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N2 - In this paper we obtain lower bounds on the radius of spatial analyticity of solutions to the Kawahara equation ut+ uux+ αuxxx+ βuxxxxx= 0 , β≠ 0 , given initial data which is analytic with a fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time t can decay no faster than 1/|t| as | t| → ∞.

AB - In this paper we obtain lower bounds on the radius of spatial analyticity of solutions to the Kawahara equation ut+ uux+ αuxxx+ βuxxxxx= 0 , β≠ 0 , given initial data which is analytic with a fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time t can decay no faster than 1/|t| as | t| → ∞.

KW - Kawahara equation

KW - Spatial analyticity

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JO - Analysis and Mathematical Physics

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Lower bounds on the radius of spatial analyticity for the Kawahara equation

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