Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts

We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten 2024-07, Vol.297 (7), p.2750-2785
Main Authors: Latushkin, Yuri, Pogan, Alin
Format: Article
Language:English
Subjects:
analytic semigroups
Banach spaces
bidomain equation
Decay rate
Electrophysiology
Lyapunov linear stability
Operators (mathematics)
Parameters
planar traveling waves
Reaction-diffusion equations
reaction–diffusion systems
Semigroups
Stability
Traveling waves
uniform exponential bounds
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c2723-e4d0a97ac7c70da4130b3513e6f7eb7bb68692d47718aca79ed26e0775a8fdcf3
container_end_page 2785
container_issue 7
container_start_page 2750
container_title Mathematische Nachrichten
container_volume 297
creator Latushkin, Yuri
Pogan, Alin
description We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.
doi_str_mv 10.1002/mana.202300273
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3076862078</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3076862078</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2723-e4d0a97ac7c70da4130b3513e6f7eb7bb68692d47718aca79ed26e0775a8fdcf3</originalsourceid><addsrcrecordid>eNqFkM1LxDAQxYMouK5ePQc8d81H22mPy-IXVD3ogreYtolkaZuatEr_e1NX9OhpZh7v9xgeQueUrCgh7LKVnVwxwng4gB-gBU0Yi1hK00O0CFoSJVn8coxOvN8RQvIc0gV63XZGW9fi0o5d7bHVWMvWNEZ97yGymQZTYa9a8-bs2Pug1biYZD929gMXplPS4adBlgEaphnqm4A5rJ3tBn-KjrRsvDr7mUu0vb563txGxePN3WZdRBUDxiMV10TmICuogNQyppyUPKFcpRpUCWWZZmnO6hiAZrKSkKuapYoAJDLTdaX5El3sc3tn30flB7Gzowvve8EJBJoRyIJrtXdVznrvlBa9M610k6BEzC2KuUXx22IA8j3waRo1_eMW9-uH9R_7BQcqd8M</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3076862078</pqid></control><display><type>article</type><title>Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts</title><source>Wiley</source><creator>Latushkin, Yuri ; Pogan, Alin</creator><creatorcontrib>Latushkin, Yuri ; Pogan, Alin</creatorcontrib><description>We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.</description><identifier>ISSN: 0025-584X</identifier><identifier>EISSN: 1522-2616</identifier><identifier>DOI: 10.1002/mana.202300273</identifier><language>eng</language><publisher>Weinheim: Wiley Subscription Services, Inc</publisher><subject>analytic semigroups ; Banach spaces ; bidomain equation ; Decay rate ; Electrophysiology ; Lyapunov linear stability ; Operators (mathematics) ; Parameters ; planar traveling waves ; Reaction-diffusion equations ; reaction–diffusion systems ; Semigroups ; Stability ; Traveling waves ; uniform exponential bounds</subject><ispartof>Mathematische Nachrichten, 2024-07, Vol.297 (7), p.2750-2785</ispartof><rights>2024 Wiley‐VCH GmbH.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2723-e4d0a97ac7c70da4130b3513e6f7eb7bb68692d47718aca79ed26e0775a8fdcf3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Latushkin, Yuri</creatorcontrib><creatorcontrib>Pogan, Alin</creatorcontrib><title>Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts</title><title>Mathematische Nachrichten</title><description>We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.</description><subject>analytic semigroups</subject><subject>Banach spaces</subject><subject>bidomain equation</subject><subject>Decay rate</subject><subject>Electrophysiology</subject><subject>Lyapunov linear stability</subject><subject>Operators (mathematics)</subject><subject>Parameters</subject><subject>planar traveling waves</subject><subject>Reaction-diffusion equations</subject><subject>reaction–diffusion systems</subject><subject>Semigroups</subject><subject>Stability</subject><subject>Traveling waves</subject><subject>uniform exponential bounds</subject><issn>0025-584X</issn><issn>1522-2616</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNqFkM1LxDAQxYMouK5ePQc8d81H22mPy-IXVD3ogreYtolkaZuatEr_e1NX9OhpZh7v9xgeQueUrCgh7LKVnVwxwng4gB-gBU0Yi1hK00O0CFoSJVn8coxOvN8RQvIc0gV63XZGW9fi0o5d7bHVWMvWNEZ97yGymQZTYa9a8-bs2Pug1biYZD929gMXplPS4adBlgEaphnqm4A5rJ3tBn-KjrRsvDr7mUu0vb563txGxePN3WZdRBUDxiMV10TmICuogNQyppyUPKFcpRpUCWWZZmnO6hiAZrKSkKuapYoAJDLTdaX5El3sc3tn30flB7Gzowvve8EJBJoRyIJrtXdVznrvlBa9M610k6BEzC2KuUXx22IA8j3waRo1_eMW9-uH9R_7BQcqd8M</recordid><startdate>202407</startdate><enddate>202407</enddate><creator>Latushkin, Yuri</creator><creator>Pogan, Alin</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202407</creationdate><title>Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts</title><author>Latushkin, Yuri ; Pogan, Alin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2723-e4d0a97ac7c70da4130b3513e6f7eb7bb68692d47718aca79ed26e0775a8fdcf3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>analytic semigroups</topic><topic>Banach spaces</topic><topic>bidomain equation</topic><topic>Decay rate</topic><topic>Electrophysiology</topic><topic>Lyapunov linear stability</topic><topic>Operators (mathematics)</topic><topic>Parameters</topic><topic>planar traveling waves</topic><topic>Reaction-diffusion equations</topic><topic>reaction–diffusion systems</topic><topic>Semigroups</topic><topic>Stability</topic><topic>Traveling waves</topic><topic>uniform exponential bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Latushkin, Yuri</creatorcontrib><creatorcontrib>Pogan, Alin</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematische Nachrichten</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Latushkin, Yuri</au><au>Pogan, Alin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts</atitle><jtitle>Mathematische Nachrichten</jtitle><date>2024-07</date><risdate>2024</risdate><volume>297</volume><issue>7</issue><spage>2750</spage><epage>2785</epage><pages>2750-2785</pages><issn>0025-584X</issn><eissn>1522-2616</eissn><abstract>We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology.</abstract><cop>Weinheim</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mana.202300273</doi><tpages>36</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0025-584X
ispartof Mathematische Nachrichten, 2024-07, Vol.297 (7), p.2750-2785
issn 0025-584X
1522-2616
language eng
recordid cdi_proquest_journals_3076862078
source Wiley
subjects analytic semigroups
Banach spaces
bidomain equation
Decay rate
Electrophysiology
Lyapunov linear stability
Operators (mathematics)
Parameters
planar traveling waves
Reaction-diffusion equations
reaction–diffusion systems
Semigroups
Stability
Traveling waves
uniform exponential bounds
title Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T16%3A07%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Uniform%20bounds%20of%20families%20of%20analytic%20semigroups%20and%20Lyapunov%20Linear%20Stability%20of%20planar%20fronts&rft.jtitle=Mathematische%20Nachrichten&rft.au=Latushkin,%20Yuri&rft.date=2024-07&rft.volume=297&rft.issue=7&rft.spage=2750&rft.epage=2785&rft.pages=2750-2785&rft.issn=0025-584X&rft.eissn=1522-2616&rft_id=info:doi/10.1002/mana.202300273&rft_dat=%3Cproquest_cross%3E3076862078%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c2723-e4d0a97ac7c70da4130b3513e6f7eb7bb68692d47718aca79ed26e0775a8fdcf3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=3076862078&rft_id=info:pmid/&rfr_iscdi=true