Fetecau, Razvan C.; Park, Hansol Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature. (English) Zbl 1514.35046 J. Geom. Anal. 33, No. 7, Paper No. 218, 39 p. (2023). MSC: 35B40 35A30 35B38 35R01 58J90 PDFBibTeX XMLCite \textit{R. C. Fetecau} and \textit{H. Park}, J. Geom. Anal. 33, No. 7, Paper No. 218, 39 p. (2023; Zbl 1514.35046) Full Text: DOI arXiv
Carrillo, José A.; Shu, Ruiwen From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials. (English) Zbl 1503.35016 Calc. Var. Partial Differ. Equ. 62, No. 1, Paper No. 28, 61 p. (2023). MSC: 35B07 35A15 35Q49 35R09 49J20 49K20 PDFBibTeX XMLCite \textit{J. A. Carrillo} and \textit{R. Shu}, Calc. Var. Partial Differ. Equ. 62, No. 1, Paper No. 28, 61 p. (2023; Zbl 1503.35016) Full Text: DOI arXiv
Fetecau, Razvan C.; Park, Hansol; Patacchini, Francesco S. Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds. (English) Zbl 1479.35006 Anal. Appl., Singap. 19, No. 6, 965-1017 (2021). MSC: 35A01 35B40 35D30 35K59 35R01 58J90 PDFBibTeX XMLCite \textit{R. C. Fetecau} et al., Anal. Appl., Singap. 19, No. 6, 965--1017 (2021; Zbl 1479.35006) Full Text: DOI arXiv
Carrillo, José A.; Fjordholm, Ulrik S.; Solem, Susanne A second-order numerical method for the aggregation equations. (English) Zbl 1452.65186 Math. Comput. 90, No. 327, 103-139 (2021). Reviewer: Victor Michel-Dansac (Strasbourg) MSC: 65M08 65M12 35B44 35D30 35R09 35R06 92C17 35Q92 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Math. Comput. 90, No. 327, 103--139 (2021; Zbl 1452.65186) Full Text: DOI arXiv Link
Carrillo, José A.; Düring, Bertram; Kreusser, Lisa Maria; Schönlieb, Carola-Bibiane Stability analysis of line patterns of an anisotropic interaction model. (English) Zbl 1430.35026 SIAM J. Appl. Dyn. Syst. 18, No. 4, 1798-1845 (2019). MSC: 35B36 35Q92 70F10 70F45 82C22 35B35 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., SIAM J. Appl. Dyn. Syst. 18, No. 4, 1798--1845 (2019; Zbl 1430.35026) Full Text: DOI arXiv
Düring, Bertram; Gottschlich, Carsten; Huckemann, Stephan; Kreusser, Lisa Maria; Schönlieb, Carola-Bibiane An anisotropic interaction model for simulating fingerprints. (English) Zbl 1420.35436 J. Math. Biol. 78, No. 7, 2171-2206 (2019). MSC: 35Q92 35B36 70F10 82C22 92C15 92C17 PDFBibTeX XMLCite \textit{B. Düring} et al., J. Math. Biol. 78, No. 7, 2171--2206 (2019; Zbl 1420.35436) Full Text: DOI arXiv
Campos Pinto, Martin; Carrillo, José A.; Charles, Frédérique; Choi, Young-Pil Convergence of a linearly transformed particle method for aggregation equations. (English) Zbl 1408.65066 Numer. Math. 139, No. 4, 743-793 (2018). MSC: 65M12 65M50 82C22 35Q70 PDFBibTeX XMLCite \textit{M. Campos Pinto} et al., Numer. Math. 139, No. 4, 743--793 (2018; Zbl 1408.65066) Full Text: DOI arXiv
Burger, Martin; Düring, Bertram; Kreusser, Lisa Maria; Markowich, Peter A.; Schönlieb, Carola-Bibiane Pattern formation of a nonlocal, anisotropic interaction model. (English) Zbl 1383.35024 Math. Models Methods Appl. Sci. 28, No. 3, 409-451 (2018). MSC: 35B36 35Q92 70F10 82C22 PDFBibTeX XMLCite \textit{M. Burger} et al., Math. Models Methods Appl. Sci. 28, No. 3, 409--451 (2018; Zbl 1383.35024) Full Text: DOI arXiv
Evers, Joep H. M.; Fetecau, Razvan C.; Sun, Weiran Small inertia regularization of an anisotropic aggregation model. (English) Zbl 1380.34076 Math. Models Methods Appl. Sci. 27, No. 10, 1795-1842 (2017). Reviewer: Vladimir Răsvan (Craiova) MSC: 34C60 34E15 65L11 91B14 34A36 PDFBibTeX XMLCite \textit{J. H. M. Evers} et al., Math. Models Methods Appl. Sci. 27, No. 10, 1795--1842 (2017; Zbl 1380.34076) Full Text: DOI arXiv
von Brecht, James H.; Uminsky, David T. Anisotropic assembly and pattern formation. (English) Zbl 1359.35191 Nonlinearity 30, No. 1, 225-273 (2017). MSC: 35Q70 35B35 37J25 70F10 70F45 35R09 PDFBibTeX XMLCite \textit{J. H. von Brecht} and \textit{D. T. Uminsky}, Nonlinearity 30, No. 1, 225--273 (2017; Zbl 1359.35191) Full Text: DOI
Evers, Joep H. M.; Kolokolnikov, Theodore Metastable states for an aggregation model with noise. (English) Zbl 1359.35201 SIAM J. Appl. Dyn. Syst. 15, No. 4, 2213-2226 (2016). MSC: 35Q92 35B40 35B20 35B36 60J60 65N75 92C15 PDFBibTeX XMLCite \textit{J. H. M. Evers} and \textit{T. Kolokolnikov}, SIAM J. Appl. Dyn. Syst. 15, No. 4, 2213--2226 (2016; Zbl 1359.35201) Full Text: DOI arXiv
Carrillo, J. A.; Delgadino, M. G.; Mellet, A. Regularity of local minimizers of the interaction energy via obstacle problems. (English) Zbl 1337.49066 Commun. Math. Phys. 343, No. 3, 747-781 (2016). MSC: 49N60 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Commun. Math. Phys. 343, No. 3, 747--781 (2016; Zbl 1337.49066) Full Text: DOI arXiv
von Brecht, James H. Localization and vector spherical harmonics. (English) Zbl 1334.33030 J. Differ. Equations 260, No. 2, 1622-1655 (2016). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33C55 42A38 35P99 PDFBibTeX XMLCite \textit{J. H. von Brecht}, J. Differ. Equations 260, No. 2, 1622--1655 (2016; Zbl 1334.33030) Full Text: DOI
Carrillo, J. A.; James, F.; Lagoutière, F.; Vauchelet, N. The Filippov characteristic flow for the aggregation equation with mildly singular potentials. (English) Zbl 1323.35005 J. Differ. Equations 260, No. 1, 304-338 (2016). MSC: 35B40 35D30 35L60 35Q92 49K20 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., J. Differ. Equations 260, No. 1, 304--338 (2016; Zbl 1323.35005) Full Text: DOI arXiv
Fetecau, R. C.; Sun, W. First-order aggregation models and zero inertia limits. (English) Zbl 1329.35320 J. Differ. Equations 259, No. 11, 6774-6802 (2015). Reviewer: Piotr Biler (Wroclaw) MSC: 35Q92 92C15 35Q70 70F45 82C21 PDFBibTeX XMLCite \textit{R. C. Fetecau} and \textit{W. Sun}, J. Differ. Equations 259, No. 11, 6774--6802 (2015; Zbl 1329.35320) Full Text: DOI arXiv
Cañizo, José A.; Carrillo, José A.; Patacchini, Francesco S. Existence of compactly supported global minimisers for the interaction energy. (English) Zbl 1317.82010 Arch. Ration. Mech. Anal. 217, No. 3, 1197-1217 (2015). MSC: 82B21 49S05 74G65 PDFBibTeX XMLCite \textit{J. A. Cañizo} et al., Arch. Ration. Mech. Anal. 217, No. 3, 1197--1217 (2015; Zbl 1317.82010) Full Text: DOI arXiv
Carrillo, José Antonio; Chipot, Michel; Huang, Yanghong On global minimizers of repulsive-attractive power-law interaction energies. (English) Zbl 1353.49002 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 372, No. 2028, Article ID 20130399, 13 p. (2014). MSC: 49J10 35Q92 35Q35 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 372, No. 2028, Article ID 20130399, 13 p. (2014; Zbl 1353.49002) Full Text: DOI arXiv
Mackey, Alan; Kolokolnikov, Theodore; Bertozzi, Andrea L. Two-species particle aggregation and stability of co-dimension one solutions. (English) Zbl 1304.35081 Discrete Contin. Dyn. Syst., Ser. B 19, No. 5, 1411-1436 (2014). MSC: 35B36 35B35 35B20 35D30 41A60 PDFBibTeX XMLCite \textit{A. Mackey} et al., Discrete Contin. Dyn. Syst., Ser. B 19, No. 5, 1411--1436 (2014; Zbl 1304.35081) Full Text: DOI
Balagué, Daniel; Carrillo, José A.; Yao, Yao Confinement for repulsive-attractive kernels. (English) Zbl 1304.35703 Discrete Contin. Dyn. Syst., Ser. B 19, No. 5, 1227-1248 (2014). MSC: 35Q92 35B40 37N25 PDFBibTeX XMLCite \textit{D. Balagué} et al., Discrete Contin. Dyn. Syst., Ser. B 19, No. 5, 1227--1248 (2014; Zbl 1304.35703) Full Text: DOI arXiv
Carrillo, J. A.; Huang, Y.; Martin, S. Explicit flock solutions for quasi-Morse potentials. (English) Zbl 1304.82049 Eur. J. Appl. Math. 25, No. 5, 553-578 (2014). MSC: 82C22 92D25 33C10 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Eur. J. Appl. Math. 25, No. 5, 553--578 (2014; Zbl 1304.82049) Full Text: DOI arXiv
Carrillo, J. A.; Huang, Yanghong; Martin, S. Nonlinear stability of flock solutions in second-order swarming models. (English) Zbl 1302.34082 Nonlinear Anal., Real World Appl. 17, 332-343 (2014). Reviewer: Svetlin Georgiev (Rousse) MSC: 34D20 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Nonlinear Anal., Real World Appl. 17, 332--343 (2014; Zbl 1302.34082) Full Text: DOI arXiv
Kolokolnikov, Theodore; Huang, Yanghong; Pavlovski, Mark Singular patterns for an aggregation model with a confining potential. (English) Zbl 1286.35036 Physica D 260, 65-76 (2013). MSC: 35B36 92D15 35B32 35B25 PDFBibTeX XMLCite \textit{T. Kolokolnikov} et al., Physica D 260, 65--76 (2013; Zbl 1286.35036) Full Text: DOI
Balagué, D.; Carrillo, J. A.; Laurent, T.; Raoul, G. Nonlocal interactions by repulsive-attractive potentials: radial ins/stability. (English) Zbl 1286.35038 Physica D 260, 5-25 (2013). MSC: 35B40 35B07 35R11 PDFBibTeX XMLCite \textit{D. Balagué} et al., Physica D 260, 5--25 (2013; Zbl 1286.35038) Full Text: DOI arXiv
Balagué, D.; Carrillo, J. A.; Laurent, T.; Raoul, G. Dimensionality of local minimizers of the interaction energy. (English) Zbl 1311.49053 Arch. Ration. Mech. Anal. 209, No. 3, 1055-1088 (2013). Reviewer: Constantin Udrişte (Bucureşti) MSC: 49K20 PDFBibTeX XMLCite \textit{D. Balagué} et al., Arch. Ration. Mech. Anal. 209, No. 3, 1055--1088 (2013; Zbl 1311.49053) Full Text: DOI arXiv
von Brecht, James H.; Bertozzi, Andrea L. Well-posedness theory for aggregation sheets. (English) Zbl 1307.58018 Commun. Math. Phys. 319, No. 2, 451-477 (2013). MSC: 58J99 PDFBibTeX XMLCite \textit{J. H. von Brecht} and \textit{A. L. Bertozzi}, Commun. Math. Phys. 319, No. 2, 451--477 (2013; Zbl 1307.58018) Full Text: DOI
von Brecht, James; Kolokolnikov, Theodore; Bertozzi, Andrea L.; Sun, Hui Swarming on random graphs. (English) Zbl 1269.82047 J. Stat. Phys. 151, No. 1-2, 150-173 (2013). MSC: 82C22 05C80 92D50 PDFBibTeX XMLCite \textit{J. von Brecht} et al., J. Stat. Phys. 151, No. 1--2, 150--173 (2013; Zbl 1269.82047) Full Text: DOI
Sun, Hui; Uminsky, David; Bertozzi, Andrea L. Stability and clustering of self-similar solutions of aggregation equations. (English) Zbl 1278.35259 J. Math. Phys. 53, No. 11, 115610, 18 p. (2012). MSC: 35R09 35B35 35C06 35B44 35Q92 PDFBibTeX XMLCite \textit{H. Sun} et al., J. Math. Phys. 53, No. 11, 115610, 18 p. (2012; Zbl 1278.35259) Full Text: DOI