ON MULTIPLICATIVE TIME-DEPENDENT PERTURBATIONS OF SEMIGROUPS AND COSINE FAMILIES GENERATORS

被引：0

作者：

Ipocoana, Erica ^{[1
]}

Taddei, Valentina ^{[2
]}

机构：

[1] Free Univ Berlin, Dept Math & Comp Sci, Arnimallee 9, D-14195 Berlin, Germany

[2] Univ Modena & Reggio Emilia, Dipartimento Sci & Metodi Ingn, Via G Amendola 2, I-42122 Reggio Emilia, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年

关键词：

Key words and phrases. Multiplicative perturbations; evolution systems; fundamental systems; Banach spaces; wave equation; EVOLUTION; EQUATION;

D O I：

10.3934/dcdss.2024154

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. In this work we aim to investigate a second order PDE modelling a vibrating string. Our strategy consists in transforming the PDE problem into a semilinear second order ODE in a suitable infinite dimensional space. Since the tension coefficient of the PDE may vary with time, the linear operator of the ODE depends on time. We therefore provide sufficient conditions guaranteeing that a suitable family of unbounded linear operators generates a fundamental system.

引用

页数：18

共 50 条

[1] MULTIPLICATIVE PERTURBATIONS OF GENERATORS OF SEMIGROUPS . PRELIMINARY REPORT
WIDGER, CF
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (04): : 665 - &
[2] TIME-DEPENDENT PERTURBATION FOR COSINE-FAMILIES IN BANACH-SPACES
SERIZAWA, H
WATANABE, M
HOUSTON JOURNAL OF MATHEMATICS, 1986, 12 (04): : 579 - 586
[3] Multiplicative Perturbations of Convoluted C-Cosine Functions and Convoluted C-Semigroups
Li, Fang
Wang, Huiwen
Zhang, Jun
JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,
[4] TIME-DEPENDENT PERTURBATIONS AT TIME-DEPENDENT LINEAR ACCRETIVE OPERATORS
FITZGIBB.WE
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (01): : A157 - A157
[5] SCATTERING BY TIME-DEPENDENT PERTURBATIONS
SCHMIDT, EJPG
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1975, 24 (10) : 925 - 935
[6] Cosine families and semigroups really differ
Adam Bobrowski
Wojciech Chojnacki
Journal of Evolution Equations, 2013, 13 : 897 - 916
[7] Cosine families and semigroups really differ
Bobrowski, Adam
Chojnacki, Wojciech
JOURNAL OF EVOLUTION EQUATIONS, 2013, 13 (04) : 897 - 916
[8] Evolution families and generators of semigroups
Jung, M
HOUSTON JOURNAL OF MATHEMATICS, 1997, 23 (02): : 357 - 383
[9] TIME-REVERSAL BY TIME-DEPENDENT PERTURBATIONS
Bal, Guillaume
Fink, Mathias
Pinaud, Olivier
SIAM JOURNAL ON APPLIED MATHEMATICS, 2019, 79 (03) : 754 - 780
[10] LOCALIZED TIME-DEPENDENT PERTURBATIONS IN METALS
BLANDIN, A
HONE, D
NOURTIER, A
JOURNAL DE PHYSIQUE LETTRES, 1975, 36 (04): : L109 - L111

← 1 2 3 4 5 →