Open AccessOn the ill-posedness result for the BBM equation
Author(s) -
Mahendra Panthee
Publication year - 2011
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2011.30.253
Subject(s) - initial value problem , well posed problem , mathematics , value (mathematics) , sense (electronics) , mathematical analysis , mathematical physics , physics , statistics , electrical engineering , engineering
We prove that the initial value problem (IVP) for the BBM equation is
ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that
associates to initial data u0 the solution u cannot be continuous at the origin from
Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.Fundação para a Ciência e a Tecnologia (FCT
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