Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ℳ of ℝ d endowed with a Riemannian metric g. We ob...

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Published inCommunications in partial differential equations Vol. 40; no. 7; pp. 1241 - 1281
Main Authors Wu, Lijiang, Slepčev, Dejan
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 03.07.2015
Taylor & Francis Ltd
Subjects
Boundaries
Equations on manifolds
Gradient flow
Gradient flows
Heterogeneity
Mathematical analysis
Nonlocal interactions
Optimal transport
Partial differential equations
Particle approximation
Stability
Uniqueness
Well-posedness of measure solutions
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Abstract We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ℳ of ℝ d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ℳ endowed with Riemannian 2-Wasserstein metric.
AbstractList We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ℳ of ℝ d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ℳ endowed with Riemannian 2-Wasserstein metric.
We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets [physics M-matrix] of R d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on [physics M-matrix] endowed with Riemannian 2-Wasserstein metric.
We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets [phmmat] of R super( )dendowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on [phmmat] endowed with Riemannian 2-Wasserstein metric.
Author Slepčev, Dejan
Wu, Lijiang
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Cites_doi 10.1016/j.aml.2012.06.023
10.1016/j.matpur.2004.11.002
10.1007/s11538-006-9088-6
10.1007/978-3-642-32160-3_1
10.1103/PhysRevLett.96.104302
10.1214/08-AIHP306
10.1088/0951-7715/24/10/002
10.1007/s002220100160
10.1137/100804504
10.1215/00127094-2010-211
10.1007/s00220-007-0288-1
10.1137/090774495
10.1103/PhysRevE.84.015203
10.1137/11081986X
10.1007/s11856-010-0001-5
10.1137/090749037
10.1007/s00526-009-0303-9
10.4310/CMS.2010.v8.n1.a4
10.1080/03605300701318955
10.1016/j.mcm.2010.03.021
10.1007/PL00001679
10.1137/S0036139903437424
10.1002/cpa.20334
10.1137/050622420
10.1007/s00205-012-0493-8
10.4171/077-1/1
10.1002/cpa.21431
10.4171/JEMS/388
10.1007/s00205-013-0644-6
10.3934/nhm.2008.3.749
10.1088/0951-7715/22/3/009
10.1371/journal.pcbi.1002642
10.1051/cocv:2008044
10.1140/epjst/e2008-00633-y
10.1142/S0218202510004921
10.1016/j.na.2011.08.057
10.1137/08071346X
10.3934/dcdsb.2012.17.1309
10.1007/978-3-540-71050-9
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  start-page: 417
  year: 2014
  ident: CIT0005
  publication-title: Diff. Int. Eqs.
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    fullname: Balagué D.
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  doi: 10.1016/j.aml.2012.06.023
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  doi: 10.1016/j.matpur.2004.11.002
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  doi: 10.1103/PhysRevLett.96.104302
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  doi: 10.1214/08-AIHP306
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  doi: 10.1137/100804504
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  doi: 10.1137/11081986X
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  doi: 10.4310/CMS.2010.v8.n1.a4
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  doi: 10.1080/03605300701318955
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  doi: 10.1007/PL00001679
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  doi: 10.1137/S0036139903437424
– ident: CIT0011
  doi: 10.1002/cpa.20334
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  doi: 10.1137/050622420
– ident: CIT0036
  doi: 10.1007/s00205-012-0493-8
– ident: CIT0015
  doi: 10.4171/077-1/1
– volume: 5
  start-page: 575
  year: 2012
  ident: CIT0003
  publication-title: Boll. Unione Mat. Ital.
  contributor:
    fullname: Ambrosio L.
– ident: CIT0027
  doi: 10.1002/cpa.21431
– volume: 171
  volume-title: Riemannian Geometry
  year: 2006
  ident: CIT0038
  contributor:
    fullname: Petersen P.
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  doi: 10.4171/JEMS/388
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  doi: 10.1007/s00205-013-0644-6
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  doi: 10.3934/nhm.2008.3.749
– volume: 25
  start-page: 417
  year: 2012
  ident: CIT0039
  publication-title: Diff. Int. Eqs.
  contributor:
    fullname: Raoul G.
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  doi: 10.1088/0951-7715/22/3/009
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  doi: 10.1371/journal.pcbi.1002642
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  doi: 10.1051/cocv:2008044
– ident: CIT0041
  doi: 10.1140/epjst/e2008-00633-y
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  year: 2007
  ident: CIT0025
  contributor:
    fullname: Fonseca I.
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  doi: 10.1142/S0218202510004921
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  doi: 10.1137/08071346X
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  doi: 10.3934/dcdsb.2012.17.1309
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  year: 2008
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  contributor:
    fullname: Ambrosio L.
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  doi: 10.1007/978-3-540-71050-9
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Snippet We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and...
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SubjectTerms Boundaries
Equations on manifolds
Gradient flow
Gradient flows
Heterogeneity
Mathematical analysis
Nonlocal interactions
Optimal transport
Partial differential equations
Particle approximation
Stability
Uniqueness
Well-posedness of measure solutions
Title Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries
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