Analyticity in partial differential equations

Himonas, A. Alexandrou; Petronilho, Gerson

doi:10.1007/s40627-020-00052-x

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2022

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Cited by 4 publications

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“…The method is powerful and has been used to establish analytic radius lower bounds for KdV equations [12,13,14,15,16], KdV-BBM equations [17,18] and other dispersive equations [19,20,21,22,23,24]. For more results on the analytic radius, we refer to the survey [25].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Improved lower bounds of analytic radius for the Benjamin-Bona-Mahony equation

Wang¹

2022

Preprint

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This paper is devoted to the spatial analyticity of the solution of the BBM equation on the real line with an analytic initial data. It is shown that the analytic radius has a lower bound like t − 2 3 as time t goes to infinity, which is an improvement of previous results. The main new ingredient is a higher order almost conservation law in analytic spaces. This is proved by introducing an equivalent analytic norm with smooth symbol and establishing some algebra identities of higher order polynomials.

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