Partial Di¤erential Equations

Michael Gil

doi:10.4171/RLM/822

Partial Di¤erential Equations

Michael Gil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English
Pages (from-to)	589-596
Number of pages	8
Journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
Volume	29
Issue number	4
DOIs	https://doi.org/10.4171/RLM/822
State	Published - 1 Jan 2018

Keywords

Banach space
Linear di¤erential equation
Stability

ASJC Scopus subject areas

General Mathematics

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10.4171/RLM/822

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title = "Partial Di¤erential Equations",

abstract = " Let A be a generator of a C 0 -semigroup in a Banach space X, and B{\dh}t{\TH} {\dh}t b 0{\TH} be a variable bounded piece-wise strongly continuous operator in X. We consider the equation dy{\dh}t{\TH}=dt ¼ {\dh}A {\th} B{\dh}t{\TH}{\TH} y{\dh}t{\TH} {\dh}t b 0{\TH}. It is assumed that the commutator K {\dh}t{\TH} ¼ AB{\dh}t{\TH} B{\dh}t{\TH}A is a bounded operator. Under that condition, exponential stability conditions are derived in terms of the commutator.",

keywords = "Banach space, Linear di¤erential equation, Stability",

author = "Michael Gil",

year = "2018",

month = jan,

day = "1",

doi = "10.4171/RLM/822",

language = "English",

volume = "29",

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journal = "Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni",

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T1 - Partial Di¤erential Equations

AU - Gil, Michael

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Banach space

KW - Linear di¤erential equation

KW - Stability

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U2 - 10.4171/RLM/822

DO - 10.4171/RLM/822

M3 - Article

AN - SCOPUS:85061819823

SN - 1120-6330

VL - 29

SP - 589

EP - 596

JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

IS - 4

ER -

Partial Di¤erential Equations

Abstract

Keywords

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