Evolution of the radius of spatial analyticity for the periodic BBM equation | Zendy

A. Alexandrou Himonas | Zendy; Gerson Petronilho | Zendy

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Evolution of the radius of spatial analyticity for the periodic BBM equation

Author(s) -

A. Alexandrou Himonas,

Gerson Petronilho

Publication year - 2019

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) - radius , mathematics , mathematical analysis , physics , mathematical physics , computer science , computer security

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.

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