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 Naf8e5fab3e7247ac849ab67fe40fd69d
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 N4bf28d22ff7047ea8b7c0f09601fc3e9
11 Na7ea1b2bcb0b4f7a8109f8f8d6424710
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 N8c389d73d9a0447298412d24864f0297
16 Nf4c91bf42e364d0fbb2a0daec0fcfdb7
17 Nfe037d60caf24ac68930e95ec18ea21c
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 N7f0367e860be4ebcadcafaf5588ee0eb
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 N4bf28d22ff7047ea8b7c0f09601fc3e9 schema:volumeNumber 157
28 rdf:type schema:PublicationVolume
29 N4e8edc21d65b44f9a35ab6365f95bf78 schema:name University of Chicago, Department of Mathematics¶5734 University Avenue, Chicago, IL 60637-1546, USA, US
30 rdf:type schema:Organization
31 N5963417c5322421a92cbc6add7784c03 rdf:first sg:person.014464755010.82
32 rdf:rest rdf:nil
33 N7f0367e860be4ebcadcafaf5588ee0eb schema:name Springer Nature - SN SciGraph project
34 rdf:type schema:Organization
35 N8c389d73d9a0447298412d24864f0297 schema:name doi
36 schema:value 10.1007/pl00004238
37 rdf:type schema:PropertyValue
38 Na7ea1b2bcb0b4f7a8109f8f8d6424710 schema:issueNumber 2
39 rdf:type schema:PublicationIssue
40 Naf8e5fab3e7247ac849ab67fe40fd69d rdf:first sg:person.01126773333.74
41 rdf:rest N5963417c5322421a92cbc6add7784c03
42 Nf4c91bf42e364d0fbb2a0daec0fcfdb7 schema:name readcube_id
43 schema:value ccf97dfa76dea407ed183c6f9f93afe8dc2d44d1f7405cc91a57c9d42f9cf96e
44 rdf:type schema:PropertyValue
45 Nfe037d60caf24ac68930e95ec18ea21c schema:name dimensions_id
46 schema:value pub.1043031733
47 rdf:type schema:PropertyValue
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 N4e8edc21d65b44f9a35ab6365f95bf78
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)


...