Spectrum of the M 5 -traveling waves
In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M 5 -model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally u...
Gespeichert in:
| Veröffentlicht in: | Mathematical modelling of natural phenomena 2020-12, Vol.15, p.66 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | 66 |
| container_title | Mathematical modelling of natural phenomena |
| container_volume | 15 |
| creator | Cruz-García, Salvador |
| description | In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M
5
-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in
L
2
(ℝ; ℂ
3
) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space
L
w
2
(ℝ; ℂ
3
) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space
L
wα
2
(ℝ; ℂ
2
) ×
L
wε
2
(ℝ; ℂ) the essential spectrum lies on {
Reλ |
| doi_str_mv | 10.1051/mmnp/2020039 |
| format | Article |
| fullrecord | <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_1051_mmnp_2020039</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1051_mmnp_2020039</sourcerecordid><originalsourceid>FETCH-LOGICAL-c122t-fef084be1b5a66c5c7386c2b4d2c97e57f7ae31fa52260e4309b5f54c0b3219f3</originalsourceid><addsrcrecordid>eNotj7tOAzEURC0EEquQjg9wQYnJvb5-7JYo4iUFUQC1ZRsbgrLJyl5A_D0bkWlmqqM5jJ0jXCFoXPT9dlhIkADUHbEGrQFhEPCYNdBZEppUe8rmtX7CFEJFAA27eB5SHMtXz3eZjx-JP3LNxVj8d9qst-_8Zxr1jJ1kv6lpfugZe729eVnei9XT3cPyeiUiSjmKnDK0KiQM2hsTdbTUmiiDepOxs0nbbH0izF5LaSBNB7qgs1YRAknsMs3Y5T83ll2tJWU3lHXvy69DcHtJt5d0B0n6AwUVQzU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Spectrum of the M 5 -traveling waves</title><source>Free E-Journal (出版社公開部分のみ）</source><source>Alma/SFX Local Collection</source><creator>Cruz-García, Salvador</creator><creatorcontrib>Cruz-García, Salvador</creatorcontrib><description>In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M
5
-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in
L
2
(ℝ; ℂ
3
) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space
L
w
2
(ℝ; ℂ
3
) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space
L
wα
2
(ℝ; ℂ
2
) ×
L
wε
2
(ℝ; ℂ) the essential spectrum lies on {
Reλ
<0}, outside the imaginary axis.</description><identifier>ISSN: 0973-5348</identifier><identifier>EISSN: 1760-6101</identifier><identifier>DOI: 10.1051/mmnp/2020039</identifier><language>eng</language><ispartof>Mathematical modelling of natural phenomena, 2020-12, Vol.15, p.66</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c122t-fef084be1b5a66c5c7386c2b4d2c97e57f7ae31fa52260e4309b5f54c0b3219f3</cites><orcidid>0000-0001-9153-657X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Cruz-García, Salvador</creatorcontrib><title>Spectrum of the M 5 -traveling waves</title><title>Mathematical modelling of natural phenomena</title><description>In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M
5
-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in
L
2
(ℝ; ℂ
3
) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space
L
w
2
(ℝ; ℂ
3
) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space
L
wα
2
(ℝ; ℂ
2
) ×
L
wε
2
(ℝ; ℂ) the essential spectrum lies on {
Reλ
<0}, outside the imaginary axis.</description><issn>0973-5348</issn><issn>1760-6101</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNotj7tOAzEURC0EEquQjg9wQYnJvb5-7JYo4iUFUQC1ZRsbgrLJyl5A_D0bkWlmqqM5jJ0jXCFoXPT9dlhIkADUHbEGrQFhEPCYNdBZEppUe8rmtX7CFEJFAA27eB5SHMtXz3eZjx-JP3LNxVj8d9qst-_8Zxr1jJ1kv6lpfugZe729eVnei9XT3cPyeiUiSjmKnDK0KiQM2hsTdbTUmiiDepOxs0nbbH0izF5LaSBNB7qgs1YRAknsMs3Y5T83ll2tJWU3lHXvy69DcHtJt5d0B0n6AwUVQzU</recordid><startdate>20201203</startdate><enddate>20201203</enddate><creator>Cruz-García, Salvador</creator><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9153-657X</orcidid></search><sort><creationdate>20201203</creationdate><title>Spectrum of the M 5 -traveling waves</title><author>Cruz-García, Salvador</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c122t-fef084be1b5a66c5c7386c2b4d2c97e57f7ae31fa52260e4309b5f54c0b3219f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cruz-García, Salvador</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical modelling of natural phenomena</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cruz-García, Salvador</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Spectrum of the M 5 -traveling waves</atitle><jtitle>Mathematical modelling of natural phenomena</jtitle><date>2020-12-03</date><risdate>2020</risdate><volume>15</volume><spage>66</spage><pages>66-</pages><issn>0973-5348</issn><eissn>1760-6101</eissn><abstract>In this paper, we study the essential spectrum of the operator obtained by linearizing at traveling waves that occur in the one-dimensional version of the M
5
-model for mesenchymal cell movement inside a directed tissue made up of highly aligned fibers. We show that traveling waves are spectrally unstable in
L
2
(ℝ; ℂ
3
) as the essential spectrum includes the imaginary axis. Tools in the proof include exponential dichotomies and Fredholm properties. We prove that a weighted space
L
w
2
(ℝ; ℂ
3
) with the same function for the tree variables of the linearized operator is no suitable to shift the essential spectrum to the left of the imaginary axis. We find a pair of appropriate weight functions whereby on the weighted space
L
wα
2
(ℝ; ℂ
2
) ×
L
wε
2
(ℝ; ℂ) the essential spectrum lies on {
Reλ
<0}, outside the imaginary axis.</abstract><doi>10.1051/mmnp/2020039</doi><orcidid>https://orcid.org/0000-0001-9153-657X</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0973-5348 |
| ispartof | Mathematical modelling of natural phenomena, 2020-12, Vol.15, p.66 |
| issn | 0973-5348 1760-6101 |
| language | eng |
| recordid | cdi_crossref_primary_10_1051_mmnp_2020039 |
| source | Free E-Journal (出版社公開部分のみ）; Alma/SFX Local Collection |
| title | Spectrum of the M 5 -traveling waves |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T15%3A41%3A43IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Spectrum%20of%20the%20M%205%20-traveling%20waves&rft.jtitle=Mathematical%20modelling%20of%20natural%20phenomena&rft.au=Cruz-Garc%C3%ADa,%20Salvador&rft.date=2020-12-03&rft.volume=15&rft.spage=66&rft.pages=66-&rft.issn=0973-5348&rft.eissn=1760-6101&rft_id=info:doi/10.1051/mmnp/2020039&rft_dat=%3Ccrossref%3E10_1051_mmnp_2020039%3C/crossref%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |