Linearized stability for nonlinear Volterra equations

Stig-Olof Londen; Wolfgang M. Ruess

doi:10.1007/s00028-016-0381-z

Linearized stability for nonlinear Volterra equations

Stig-Olof Londen, Wolfgang M. Ruess

Department of Mathematics and Systems Analysis

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

2 Citations (Scopus)

Abstract

In the context of the nonlinear Volterra equation u(t)+∫0tb(t-s)Au(s)ds∋u0,t≥ 0 , with A⊂ X× X an m- α-accretive operator in a Banach space X, and b a completely positive kernel, we establish a principle of linearized stability of an equilibrium solution u_e under the assumption of the existence of a resolvent-differential A~ ⊂ X× X of A at u_e with the property that (A~ - ωI) is accretive for some ω> 0.

Original language	English
Pages (from-to)	473-483
Number of pages	11
Journal	Journal of Evolution Equations
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s00028-016-0381-z
Publication status	Published - 1 Mar 2017
MoE publication type	A1 Journal article-refereed

Keywords

Accretive operators
Linearized stability
Nonlinear Volterra equations

Access to Document

10.1007/s00028-016-0381-z

Cite this

@article{21df7e7e5d26429bbb0f8c9e89d960c8,

title = "Linearized stability for nonlinear Volterra equations",

abstract = "In the context of the nonlinear Volterra equation u(t)+∫0tb(t-s)Au(s)ds∋u0,t≥ 0 , with A⊂ X× X an m- α-accretive operator in a Banach space X, and b a completely positive kernel, we establish a principle of linearized stability of an equilibrium solution ue under the assumption of the existence of a resolvent-differential A~ ⊂ X× X of A at ue with the property that (A~ - ωI) is accretive for some ω> 0.",

keywords = "Accretive operators, Linearized stability, Nonlinear Volterra equations",

author = "Stig-Olof Londen and Ruess, {Wolfgang M.}",

year = "2017",

month = mar,

day = "1",

doi = "10.1007/s00028-016-0381-z",

language = "English",

volume = "17",

pages = "473--483",

journal = "Journal of Evolution Equations",

issn = "1424-3199",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - Linearized stability for nonlinear Volterra equations

AU - Londen, Stig-Olof

AU - Ruess, Wolfgang M.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - In the context of the nonlinear Volterra equation u(t)+∫0tb(t-s)Au(s)ds∋u0,t≥ 0 , with A⊂ X× X an m- α-accretive operator in a Banach space X, and b a completely positive kernel, we establish a principle of linearized stability of an equilibrium solution ue under the assumption of the existence of a resolvent-differential A~ ⊂ X× X of A at ue with the property that (A~ - ωI) is accretive for some ω> 0.

AB - In the context of the nonlinear Volterra equation u(t)+∫0tb(t-s)Au(s)ds∋u0,t≥ 0 , with A⊂ X× X an m- α-accretive operator in a Banach space X, and b a completely positive kernel, we establish a principle of linearized stability of an equilibrium solution ue under the assumption of the existence of a resolvent-differential A~ ⊂ X× X of A at ue with the property that (A~ - ωI) is accretive for some ω> 0.

KW - Accretive operators

KW - Linearized stability

KW - Nonlinear Volterra equations

UR - http://www.scopus.com/inward/record.url?scp=84995532837&partnerID=8YFLogxK

U2 - 10.1007/s00028-016-0381-z

DO - 10.1007/s00028-016-0381-z

M3 - Article

AN - SCOPUS:84995532837

SN - 1424-3199

VL - 17

SP - 473

EP - 483

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

IS - 1

ER -

Linearized stability for nonlinear Volterra equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this