Partial Di¤erential Equations

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Abstract

Let A be a generator of a C 0 -semigroup in a Banach space X, and BðtÞ ðt b 0Þ be a variable bounded piece-wise strongly continuous operator in X. We consider the equation dyðtÞ=dt ¼ ðA þ BðtÞÞ yðtÞ ðt b 0Þ. It is assumed that the commutator K ðtÞ ¼ ABðtÞ BðtÞA is a bounded operator. Under that condition, exponential stability conditions are derived in terms of the commutator.

Original languageEnglish
Pages (from-to)589-596
Number of pages8
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
Volume29
Issue number4
DOIs
StatePublished - 1 Jan 2018

Keywords

  • Banach space
  • Linear di¤erential equation
  • Stability

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