Open AccessEvolution of the radius of spatial analyticity for the periodic BBM equation
Author(s) -
A. Alexandrou Himonas,
Gerson Petronilho
Publication year - 2020
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14942
Subject(s) - algorithm , computer science , artificial intelligence
The Cauchy problem of the Benjamin-Bona-Mahony (BBM) equation with initial data u 0 u_0 that are analytic on the torus and have uniform radius of analyticity r 0 r_0 is considered, and the evolution of the radius of spatial analyticity r ( t ) r(t) of the solution u ( t ) u(t) at any future time t t is examined. It is shown that the size of the radius of spatial analyticity persists for some time and after that it evolves in a such a way that its size at any time t t is bounded below by c t − 1 c t^{-1} for some c > 0 c>0 . The optimality of this bound remains an open question.