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On a nonlocal aggregation model with nonlinear diffusion
1. | Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, United States, United States |
[1] |
Martin Burger, Marco Di Francesco. Large time behavior of nonlocal aggregation models with nonlinear diffusion. Networks and Heterogeneous Media, 2008, 3 (4) : 749-785. doi: 10.3934/nhm.2008.3.749 |
[2] |
Jacob Bedrossian, Nancy Rodríguez. Inhomogeneous Patlak-Keller-Segel models and aggregation equations with nonlinear diffusion in $\mathbb{R}^d$. Discrete and Continuous Dynamical Systems - B, 2014, 19 (5) : 1279-1309. doi: 10.3934/dcdsb.2014.19.1279 |
[3] |
Yuming Paul Zhang. On a class of diffusion-aggregation equations. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 907-932. doi: 10.3934/dcds.2020066 |
[4] |
Aníbal Rodríguez-Bernal, Silvia Sastre-Gómez. Nonlinear nonlocal reaction-diffusion problem with local reaction. Discrete and Continuous Dynamical Systems, 2022, 42 (4) : 1731-1765. doi: 10.3934/dcds.2021170 |
[5] |
Andrea L. Bertozzi, Dejan Slepcev. Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1617-1637. doi: 10.3934/cpaa.2010.9.1617 |
[6] |
Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1579-1613. doi: 10.3934/dcdsb.2020174 |
[7] |
Georg Hetzer, Wenxian Shen. Preface: Special issue on dissipative systems and applications with emphasis on nonlocal or nonlinear diffusion problems. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : i-iii. doi: 10.3934/dcds.2015.35.4i |
[8] |
Costică Moroşanu, Bianca Satco. Qualitative and quantitative analysis for a nonlocal and nonlinear reaction-diffusion problem with in-homogeneous Neumann boundary conditions. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022042 |
[9] |
Philip K. Maini, Luisa Malaguti, Cristina Marcelli, Serena Matucci. Diffusion-aggregation processes with mono-stable reaction terms. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1175-1189. doi: 10.3934/dcdsb.2006.6.1175 |
[10] |
Jan Haškovec, Dietmar Oelz. A free boundary problem for aggregation by short range sensing and differentiated diffusion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1461-1480. doi: 10.3934/dcdsb.2015.20.1461 |
[11] |
Mikhail Kuzmin, Stefano Ruggerini. Front propagation in diffusion-aggregation models with bi-stable reaction. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 819-833. doi: 10.3934/dcdsb.2011.16.819 |
[12] |
Simone Fagioli, Yahya Jaafra. Multiple patterns formation for an aggregation/diffusion predator-prey system. Networks and Heterogeneous Media, 2021, 16 (3) : 377-411. doi: 10.3934/nhm.2021010 |
[13] |
Jiakou Wang, Margaret J. Slattery, Meghan Henty Hoskins, Shile Liang, Cheng Dong, Qiang Du. Monte carlo simulation of heterotypic cell aggregation in nonlinear shear flow. Mathematical Biosciences & Engineering, 2006, 3 (4) : 683-696. doi: 10.3934/mbe.2006.3.683 |
[14] |
Armel Ovono Andami. From local to nonlocal in a diffusion model. Conference Publications, 2011, 2011 (Special) : 54-60. doi: 10.3934/proc.2011.2011.54 |
[15] |
J. García-Melián, Julio D. Rossi. A logistic equation with refuge and nonlocal diffusion. Communications on Pure and Applied Analysis, 2009, 8 (6) : 2037-2053. doi: 10.3934/cpaa.2009.8.2037 |
[16] |
Elisabeth Logak, Isabelle Passat. An epidemic model with nonlocal diffusion on networks. Networks and Heterogeneous Media, 2016, 11 (4) : 693-719. doi: 10.3934/nhm.2016014 |
[17] |
Laurent Desvillettes, Michèle Grillot, Philippe Grillot, Simona Mancini. Study of a degenerate reaction-diffusion system arising in particle dynamics with aggregation effects. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4675-4692. doi: 10.3934/dcds.2018205 |
[18] |
Hui Huang, Jian-Guo Liu. Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3463-3478. doi: 10.3934/dcdsb.2016107 |
[19] |
Meng Zhao, Wantong Li, Yihong Du. The effect of nonlocal reaction in an epidemic model with nonlocal diffusion and free boundaries. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4599-4620. doi: 10.3934/cpaa.2020208 |
[20] |
Anouar El Harrak, Amal Bergam, Tri Nguyen-Huu, Pierre Auger, Rachid Mchich. Application of aggregation of variables methods to a class of two-time reaction-diffusion-chemotaxis models of spatially structured populations with constant diffusion. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2163-2181. doi: 10.3934/dcdss.2021055 |
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