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On the radius of spatial analyticity for the modified Kawahara equation on the line
Author(s) -
Petronilho Gerson,
Leal da Silva Priscila
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800394
Subject(s) - mathematics , holomorphic function , radius , line (geometry) , initial value problem , mathematical analysis , type (biology) , cauchy distribution , analytic function , cauchy problem , constant (computer programming) , pure mathematics , geometry , ecology , computer security , computer science , biology , programming language
First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial datau 0 ( x )that can be extended as holomorphic functions in a strip around the x ‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity r ( t ) given by r ( t ) ≥ c t − ( 4 + δ ), where δ > 0 can be taken arbitrarily small and c is a positive constant.