Peletier, Mark; Gavish, Nir; Nyquist, Pierre Large deviations and gradient flows for the Brownian one-dimensional hard-rod system. (English) Zbl 1506.60041 Potential Anal. 58, No. 1, 71-121 (2023). MSC: 60F10 60G51 35K45 35Q82 35Q70 82C41 PDFBibTeX XMLCite \textit{M. Peletier} et al., Potential Anal. 58, No. 1, 71--121 (2023; Zbl 1506.60041) Full Text: DOI arXiv
Bruna, Maria; Burger, Martin; Pietschmann, Jan-Frederik; Wolfram, Marie-Therese Active crowds. (English) Zbl 07625086 Bellomo, Nicola (ed.) et al., Active particles. Volume 3. Advances in theory, models, and applications. Cham: Birkhäuser. Model. Simul. Sci. Eng. Technol., 35-73 (2022). MSC: 76A30 76-10 91D10 PDFBibTeX XMLCite \textit{M. Bruna} et al., in: Active particles. Volume 3. Advances in theory, models, and applications. Cham: Birkhäuser. 35--73 (2022; Zbl 07625086) Full Text: DOI arXiv
Alasio, Luca; Bruna, Maria; Fagioli, Simone; Schulz, Simon Existence and regularity for a system of porous medium equations with small cross-diffusion and nonlocal drifts. (English) Zbl 1510.35162 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 223, Article ID 113064, 49 p. (2022). Reviewer: Pierre-Étienne Druet (Darmstadt) MSC: 35K61 35K59 35K51 35D30 35Q92 PDFBibTeX XMLCite \textit{L. Alasio} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 223, Article ID 113064, 49 p. (2022; Zbl 1510.35162) Full Text: DOI arXiv
Miles, Christopher E.; Zhu, Jie; Mogilner, Alex Mechanical torque promotes bipolarity of the mitotic spindle through multi-centrosomal clustering. (English) Zbl 1481.92039 Bull. Math. Biol. 84, No. 2, Paper No. 29, 19 p. (2022). MSC: 92C37 45K05 PDFBibTeX XMLCite \textit{C. E. Miles} et al., Bull. Math. Biol. 84, No. 2, Paper No. 29, 19 p. (2022; Zbl 1481.92039) Full Text: DOI DOI
Bruna, M.; Burger, M.; Carrillo, J. A. Coarse graining of a Fokker-Planck equation with excluded volume effects preserving the gradient flow structure. (English) Zbl 1510.35339 Eur. J. Appl. Math. 32, No. 4, 711-745 (2021). Reviewer: Mohamed Majdoub (Dammam) MSC: 35Q84 35K55 49K20 60J70 35C20 35A15 35B40 PDFBibTeX XMLCite \textit{M. Bruna} et al., Eur. J. Appl. Math. 32, No. 4, 711--745 (2021; Zbl 1510.35339) Full Text: DOI arXiv
Alasio, Luca; Ranetbauer, Helene; Schmidtchen, Markus; Wolfram, Marie-Therese Trend to equilibrium for systems with small cross-diffusion. (English) Zbl 1466.35027 ESAIM, Math. Model. Numer. Anal. 54, No. 5, 1661-1688 (2020). MSC: 35B40 35B45 35K51 35K59 65N08 PDFBibTeX XMLCite \textit{L. Alasio} et al., ESAIM, Math. Model. Numer. Anal. 54, No. 5, 1661--1688 (2020; Zbl 1466.35027) Full Text: DOI arXiv
Murphy, Ryan J.; Buenzli, Pascal R.; Baker, Ruth E.; Simpson, Matthew J. Mechanical cell competition in heterogeneous epithelial tissues. (English) Zbl 1464.35373 Bull. Math. Biol. 82, No. 10, Paper No. 130, 26 p. (2020). MSC: 35Q92 92C17 92C15 92C37 82C21 82C22 PDFBibTeX XMLCite \textit{R. J. Murphy} et al., Bull. Math. Biol. 82, No. 10, Paper No. 130, 26 p. (2020; Zbl 1464.35373) Full Text: DOI DOI
Ducrot, Arnaud; Manceau, David A one-dimensional logistic like equation with nonlinear and nonlocal diffusion: strong convergence to equilibrium. (English) Zbl 1441.35048 Proc. Am. Math. Soc. 148, No. 8, 3381-3392 (2020). MSC: 35B40 35B35 35K20 35R09 35Q92 PDFBibTeX XMLCite \textit{A. Ducrot} and \textit{D. Manceau}, Proc. Am. Math. Soc. 148, No. 8, 3381--3392 (2020; Zbl 1441.35048) Full Text: DOI
Murphy, R. J.; Buenzli, P. R.; Baker, R. E.; Simpson, M. J. A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation. (English) Zbl 1472.92063 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2227, Article ID 20180838, 17 p. (2019). MSC: 92C17 PDFBibTeX XMLCite \textit{R. J. Murphy} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 475, No. 2227, Article ID 20180838, 17 p. (2019; Zbl 1472.92063) Full Text: DOI
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
Flandoli, Franco; Leimbach, Matti; Olivera, Christian Uniform convergence of proliferating particles to the FKPP equation. (English) Zbl 1433.60089 J. Math. Anal. Appl. 473, No. 1, 27-52 (2019). MSC: 60K35 60J60 60H15 PDFBibTeX XMLCite \textit{F. Flandoli} et al., J. Math. Anal. Appl. 473, No. 1, 27--52 (2019; Zbl 1433.60089) Full Text: DOI arXiv
Klar, Axel; Tiwari, Sudarshan A multiscale particle method for mean field equations: the general case. (English) Zbl 1412.82025 Multiscale Model. Simul. 17, No. 1, 233-259 (2019). MSC: 82C21 82C22 65N75 82-08 PDFBibTeX XMLCite \textit{A. Klar} and \textit{S. Tiwari}, Multiscale Model. Simul. 17, No. 1, 233--259 (2019; Zbl 1412.82025) Full Text: DOI arXiv
Chertock, Alina; Tan, Changhui; Yan, Bokai An asymptotic preserving scheme for kinetic models with singular limit. (English) Zbl 1405.82025 Kinet. Relat. Models 11, No. 4, 735-756 (2018). MSC: 82C40 82C80 35L65 65M08 PDFBibTeX XMLCite \textit{A. Chertock} et al., Kinet. Relat. Models 11, No. 4, 735--756 (2018; Zbl 1405.82025) 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
Ngamsaad, Waipot; Suantai, Suthep Mechanically-driven spreading of bacterial populations. (English) Zbl 1510.92130 Commun. Nonlinear Sci. Numer. Simul. 35, 88-96 (2016). MSC: 92C99 PDFBibTeX XMLCite \textit{W. Ngamsaad} and \textit{S. Suantai}, Commun. Nonlinear Sci. Numer. Simul. 35, 88--96 (2016; Zbl 1510.92130) Full Text: DOI arXiv
Flandoli, Franco; Leimbach, Matti Mean field limit with proliferation. (English) Zbl 1353.60085 Discrete Contin. Dyn. Syst., Ser. B 21, No. 9, 3029-3052 (2016). MSC: 60K35 60F17 35K57 35K58 PDFBibTeX XMLCite \textit{F. Flandoli} and \textit{M. Leimbach}, Discrete Contin. Dyn. Syst., Ser. B 21, No. 9, 3029--3052 (2016; Zbl 1353.60085) Full Text: DOI
Bernoff, Andrew J.; Topaz, Chad M. Biological aggregation driven by social and environmental factors: a nonlocal model and its degenerate Cahn-Hilliard approximation. (English) Zbl 1351.35228 SIAM J. Appl. Dyn. Syst. 15, No. 3, 1528-1562 (2016). MSC: 35Q92 92D50 92C15 35R09 45K05 PDFBibTeX XMLCite \textit{A. J. Bernoff} and \textit{C. M. Topaz}, SIAM J. Appl. Dyn. Syst. 15, No. 3, 1528--1562 (2016; Zbl 1351.35228) Full Text: DOI arXiv
Bianca, Carlo; Dogbe, Christian Mean-field limit of a microscopic individual-based model describing collective motions. (English) Zbl 1421.82025 J. Nonlinear Math. Phys. 22, No. 1, 117-143 (2015). MSC: 82C22 35Q35 60K35 35Q83 PDFBibTeX XMLCite \textit{C. Bianca} and \textit{C. Dogbe}, J. Nonlinear Math. Phys. 22, No. 1, 117--143 (2015; Zbl 1421.82025) Full Text: DOI
Choksi, Rustum; Fetecau, Razvan C.; Topaloglu, Ihsan On minimizers of interaction functionals with competing attractive and repulsive potentials. (English) Zbl 1329.49019 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 6, 1283-1305 (2015). MSC: 49J45 35A15 35B36 PDFBibTeX XMLCite \textit{R. Choksi} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 6, 1283--1305 (2015; Zbl 1329.49019) Full Text: DOI
Carrillo, José A.; Eftimie, Raluca; Hoffmann, Franca Non-local kinetic and macroscopic models for self-organised animal aggregations. (English) Zbl 1330.35465 Kinet. Relat. Models 8, No. 3, 413-441 (2015). MSC: 35Q92 35L40 35L65 35K55 92D50 82C40 65M06 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Kinet. Relat. Models 8, No. 3, 413--441 (2015; Zbl 1330.35465) 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
Middleton, Alistair M.; Fleck, Christian; Grima, Ramon A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion. (English) Zbl 1412.92025 J. Theor. Biol. 359, 220-232 (2014). MSC: 92C17 35Q92 PDFBibTeX XMLCite \textit{A. M. Middleton} et al., J. Theor. Biol. 359, 220--232 (2014; Zbl 1412.92025) Full Text: DOI
Celiński, Rafał Stability of solutions to aggregation equation in bounded domains. (English) Zbl 1364.35159 Appl. Math. Comput. 228, 49-58 (2014). MSC: 35K59 35K20 35B35 35A01 PDFBibTeX XMLCite \textit{R. Celiński}, Appl. Math. Comput. 228, 49--58 (2014; Zbl 1364.35159) Full Text: DOI arXiv
Klar, A.; Tiwari, S. A multiscale meshfree method for macroscopic approximations of interacting particle systems. (English) Zbl 1317.82029 Multiscale Model. Simul. 12, No. 3, 1167-1192 (2014). MSC: 82C21 82C22 65N75 82-08 PDFBibTeX XMLCite \textit{A. Klar} and \textit{S. Tiwari}, Multiscale Model. Simul. 12, No. 3, 1167--1192 (2014; Zbl 1317.82029) Full Text: DOI
Bruna, Maria; Chapman, S. Jonathan Diffusion of finite-size particles in confined geometries. (English) Zbl 1297.92022 Bull. Math. Biol. 76, No. 4, 947-982 (2014); erratum ibid. 76, No. 4, 983 (2014). MSC: 92C35 60J70 PDFBibTeX XMLCite \textit{M. Bruna} and \textit{S. J. Chapman}, Bull. Math. Biol. 76, No. 4, 947--982 (2014; Zbl 1297.92022) Full Text: DOI arXiv
Bodnar, M.; Velázquez, J. J. L. Friction dominated dynamics of interacting particles locally close to a crystallographic lattice. (English) Zbl 1275.35123 Math. Methods Appl. Sci. 36, No. 10, 1206-1228 (2013). MSC: 35K59 70F40 70F45 74B15 74B20 35R11 PDFBibTeX XMLCite \textit{M. Bodnar} and \textit{J. J. L. Velázquez}, Math. Methods Appl. Sci. 36, No. 10, 1206--1228 (2013; Zbl 1275.35123) Full Text: DOI
Green, J. E. F.; Bassom, Andrew P.; Friedman, Avner A mathematical model for cell-induced gel compaction in vitro. (English) Zbl 1257.92018 Math. Models Methods Appl. Sci. 23, No. 1, 127-163 (2013). MSC: 92C35 92C37 65C20 PDFBibTeX XMLCite \textit{J. E. F. Green} et al., Math. Models Methods Appl. Sci. 23, No. 1, 127--163 (2013; Zbl 1257.92018) Full Text: DOI
Celiński, Rafał Asymptotic behaviour in a one dimensional model of interacting particles. (English) Zbl 1237.35083 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 1972-1979 (2012). MSC: 35K15 35B40 92C17 PDFBibTeX XMLCite \textit{R. Celiński}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 1972--1979 (2012; Zbl 1237.35083) Full Text: DOI arXiv
Fellner, Klemens; Raoul, Gaël Stability of stationary states of non-local equations with singular interaction potentials. (English) Zbl 1219.35342 Math. Comput. Modelling 53, No. 7-8, 1436-1450 (2011). MSC: 35R09 35B35 65M06 PDFBibTeX XMLCite \textit{K. Fellner} and \textit{G. Raoul}, Math. Comput. Modelling 53, No. 7--8, 1436--1450 (2011; Zbl 1219.35342) Full Text: DOI
Green, J. E. F.; Waters, S. L.; Whiteley, J. P.; Edelstein-Keshet, L.; Shakesheff, K. M.; Byrne, H. M. Non-local models for the formation of hepatocyte-stellate cell aggregates. (English) Zbl 1410.92025 J. Theor. Biol. 267, No. 1, 106-120 (2010). MSC: 92C17 35Q92 PDFBibTeX XMLCite \textit{J. E. F. Green} et al., J. Theor. Biol. 267, No. 1, 106--120 (2010; Zbl 1410.92025) Full Text: DOI
Li, Dong; Rodrigo, José L. Wellposedness and regularity of solutions of an aggregation equation. (English) Zbl 1197.35012 Rev. Mat. Iberoam. 26, No. 1, 261-294 (2010). Reviewer: Yaping Liu (Pittsburg) MSC: 35A01 35A02 35B45 35R11 35B65 PDFBibTeX XMLCite \textit{D. Li} and \textit{J. L. Rodrigo}, Rev. Mat. Iberoam. 26, No. 1, 261--294 (2010; Zbl 1197.35012) Full Text: DOI Euclid
Li, Dong; Rodrigo, Jose Finite-time singularities of an aggregation equation in \(\mathbb R^n\) with fractional dissipation. (English) Zbl 1178.35083 Commun. Math. Phys. 287, No. 2, 687-703 (2009). MSC: 35B44 35G25 26A33 PDFBibTeX XMLCite \textit{D. Li} and \textit{J. Rodrigo}, Commun. Math. Phys. 287, No. 2, 687--703 (2009; Zbl 1178.35083) Full Text: DOI
Li, Dong; Rodrigo, Jose L. Refined blowup criteria and nonsymmetric blowup of an aggregation equation. (English) Zbl 1168.35037 Adv. Math. 220, No. 6, 1717-1738 (2009). MSC: 35Q35 35B40 35B45 35R10 PDFBibTeX XMLCite \textit{D. Li} and \textit{J. L. Rodrigo}, Adv. Math. 220, No. 6, 1717--1738 (2009; Zbl 1168.35037) Full Text: DOI
Laurent, Thomas Local and global existence for an aggregation equation. (English) Zbl 1132.35088 Commun. Partial Differ. Equations 32, No. 12, 1941-1964 (2007). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35R10 35K15 PDFBibTeX XMLCite \textit{T. Laurent}, Commun. Partial Differ. Equations 32, No. 12, 1941--1964 (2007; Zbl 1132.35088) Full Text: DOI
Chalub, Fabio; Dolak-Struss, Yasmin; Markowich, Peter; Oelz, Dietmar; Schmeiser, Christian; Soreff, Alexander Model hierarchies for cell aggregation by chemotaxis. (English) Zbl 1094.92009 Math. Models Methods Appl. Sci. 16, No. 7, Suppl., 1173-1197 (2006). MSC: 92C17 35K57 60H15 35Q92 60J70 PDFBibTeX XMLCite \textit{F. Chalub} et al., Math. Models Methods Appl. Sci. 16, No. 7, 1173--1197 (2006; Zbl 1094.92009) Full Text: DOI
Bodnar, M.; Velazquez, J. J. L. An integro-differential equation arising as a limit of individual cell-based models. (English) Zbl 1089.45002 J. Differ. Equations 222, No. 2, 341-380 (2006). Reviewer: Sebastian Anita (Iaşi) MSC: 45K05 92D25 45M05 PDFBibTeX XMLCite \textit{M. Bodnar} and \textit{J. J. L. Velazquez}, J. Differ. Equations 222, No. 2, 341--380 (2006; Zbl 1089.45002) Full Text: DOI Link