Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2001-04

AUTHORS

François Hamel, Nikolaï Nadirashvili

ABSTRACT

This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝN:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} where f is a C2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts. More... »

PAGES

91-163

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/pl00004238

DOI

http://dx.doi.org/10.1007/pl00004238

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1043031733


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "French National Centre for Scientific Research", 
          "id": "https://www.grid.ac/institutes/grid.4444.0", 
          "name": [
            "CNRS, Universit\u00e9 Pierre et Marie Curie\u00b6Laboratoire d'Analyse Num\u00e9rique, B.C. 187\u00b64 place Jussieu, 75252 Paris Cedex 05, France, FR"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hamel", 
        "givenName": "Fran\u00e7ois", 
        "id": "sg:person.01126773333.74", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01126773333.74"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "University of Chicago, Department of Mathematics\u00b65734 University Avenue, Chicago, IL 60637-1546, USA, US"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Nadirashvili", 
        "givenName": "Nikola\u00ef", 
        "id": "sg:person.014464755010.82", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014464755010.82"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2001-04", 
    "datePublishedReg": "2001-04-01", 
    "description": "This paper is devoted to time-global solutions of the Fisher-KPP equation in \u211dN:\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}\\end{document} where f is a C2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/pl00004238", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1047617", 
        "issn": [
          "0003-9527", 
          "1432-0673"
        ], 
        "name": "Archive for Rational Mechanics and Analysis", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "157"
      }
    ], 
    "name": "Travelling Fronts and Entire Solutions\u00b6of the Fisher-KPP Equation in \u211dN", 
    "pagination": "91-163", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "ccf97dfa76dea407ed183c6f9f93afe8dc2d44d1f7405cc91a57c9d42f9cf96e"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/pl00004238"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1043031733"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/pl00004238", 
      "https://app.dimensions.ai/details/publication/pub.1043031733"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T23:25", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8693_00000515.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2FPL00004238"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/pl00004238'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/pl00004238'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/pl00004238'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/pl00004238'


 

This table displays all metadata directly associated to this object as RDF triples.

70 TRIPLES      20 PREDICATES      27 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/pl00004238 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N31e1a97e167b4ef8a59c4b97641b029f
4 schema:datePublished 2001-04
5 schema:datePublishedReg 2001-04-01
6 schema:description This paper is devoted to time-global solutions of the Fisher-KPP equation in ℝN:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} where f is a C2 concave function on [0,1] such that f(0)=f(1)=0 and f>0 on (0,1). It is well known that this equation admits a finite-dimensional manifold of planar travelling-fronts solutions. By considering the mixing of any density of travelling fronts, we prove the existence of an infinite-dimensional manifold of solutions. In particular, there are infinite-dimensional manifolds of (nonplanar) travelling fronts and radial solutions. Furthermore, up to an additional assumption, a given solution u can be represented in terms of such a mixing of travelling fronts.
7 schema:genre research_article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N31d6fe774e284aeca539f263bc9d4988
11 N43f894be5e7441c69621bea07f56c24a
12 sg:journal.1047617
13 schema:name Travelling Fronts and Entire Solutions¶of the Fisher-KPP Equation in ℝN
14 schema:pagination 91-163
15 schema:productId N6e530b5f7e024c02819eff94aed8a1de
16 Nd676f0a380d74cdbbec99c9376aa1cea
17 Nf066add9fcf94b43999542cd764afa77
18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043031733
19 https://doi.org/10.1007/pl00004238
20 schema:sdDatePublished 2019-04-10T23:25
21 schema:sdLicense https://scigraph.springernature.com/explorer/license/
22 schema:sdPublisher N2dd08af51200414199b2e0fedc959b41
23 schema:url http://link.springer.com/10.1007%2FPL00004238
24 sgo:license sg:explorer/license/
25 sgo:sdDataset articles
26 rdf:type schema:ScholarlyArticle
27 N045caecf02cd4116911bea6235826679 rdf:first sg:person.014464755010.82
28 rdf:rest rdf:nil
29 N2dd08af51200414199b2e0fedc959b41 schema:name Springer Nature - SN SciGraph project
30 rdf:type schema:Organization
31 N31d6fe774e284aeca539f263bc9d4988 schema:issueNumber 2
32 rdf:type schema:PublicationIssue
33 N31e1a97e167b4ef8a59c4b97641b029f rdf:first sg:person.01126773333.74
34 rdf:rest N045caecf02cd4116911bea6235826679
35 N43f894be5e7441c69621bea07f56c24a schema:volumeNumber 157
36 rdf:type schema:PublicationVolume
37 N6e530b5f7e024c02819eff94aed8a1de schema:name doi
38 schema:value 10.1007/pl00004238
39 rdf:type schema:PropertyValue
40 Nd676f0a380d74cdbbec99c9376aa1cea schema:name dimensions_id
41 schema:value pub.1043031733
42 rdf:type schema:PropertyValue
43 Nf066add9fcf94b43999542cd764afa77 schema:name readcube_id
44 schema:value ccf97dfa76dea407ed183c6f9f93afe8dc2d44d1f7405cc91a57c9d42f9cf96e
45 rdf:type schema:PropertyValue
46 Nffa2925d9f2a4c08ab0d787324fe8796 schema:name University of Chicago, Department of Mathematics¶5734 University Avenue, Chicago, IL 60637-1546, USA, US
47 rdf:type schema:Organization
48 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
49 schema:name Mathematical Sciences
50 rdf:type schema:DefinedTerm
51 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
52 schema:name Pure Mathematics
53 rdf:type schema:DefinedTerm
54 sg:journal.1047617 schema:issn 0003-9527
55 1432-0673
56 schema:name Archive for Rational Mechanics and Analysis
57 rdf:type schema:Periodical
58 sg:person.01126773333.74 schema:affiliation https://www.grid.ac/institutes/grid.4444.0
59 schema:familyName Hamel
60 schema:givenName François
61 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01126773333.74
62 rdf:type schema:Person
63 sg:person.014464755010.82 schema:affiliation Nffa2925d9f2a4c08ab0d787324fe8796
64 schema:familyName Nadirashvili
65 schema:givenName Nikolaï
66 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014464755010.82
67 rdf:type schema:Person
68 https://www.grid.ac/institutes/grid.4444.0 schema:alternateName French National Centre for Scientific Research
69 schema:name CNRS, Université Pierre et Marie Curie¶Laboratoire d'Analyse Numérique, B.C. 187¶4 place Jussieu, 75252 Paris Cedex 05, France, FR
70 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...