• Previous Article
    Global dynamics of the periodic un-stirred chemostat with a toxin-producing competitor
  • CPAA Home
  • This Issue
  • Next Article
    Structure of the set of bounded solutions for a class of nonautonomous second order differential equations
November  2010, 9(6): 1617-1637. doi: 10.3934/cpaa.2010.9.1617

Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion

1. 

Department of Mathematics, UCLA, Los Angeles, CA, 90095, United States

2. 

Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA, 15213, United States

Received  October 2009 Revised  May 2010 Published  August 2010

We present an energy-methods-based proof of the existence and uniqueness of solutions of a nonlocal aggregation equation with degenerate diffusion. The equation we study is relevant to models of biological aggregation.
Citation: 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
[1]

Dong Li, Xiaoyi Zhang. On a nonlocal aggregation model with nonlinear diffusion. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 301-323. doi: 10.3934/dcds.2010.27.301

[2]

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

[3]

José A. Carrillo, Bertram Düring, Lisa Maria Kreusser, Carola-Bibiane Schönlieb. Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 3985-4012. doi: 10.3934/dcds.2021025

[4]

Francesco S. Patacchini, Dejan Slepčev. The nonlocal-interaction equation near attracting manifolds. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 903-929. doi: 10.3934/dcds.2021142

[5]

José A. Carrillo, Dejan Slepčev, Lijiang Wu. Nonlocal-interaction equations on uniformly prox-regular sets. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1209-1247. doi: 10.3934/dcds.2016.36.1209

[6]

Marco Di Francesco, Yahya Jaafra. Multiple large-time behavior of nonlocal interaction equations with quadratic diffusion. Kinetic and Related Models, 2019, 12 (2) : 303-322. doi: 10.3934/krm.2019013

[7]

Alexander Pankov. Traveling waves in Fermi-Pasta-Ulam chains with nonlocal interaction. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2097-2113. doi: 10.3934/dcdss.2019135

[8]

Ciprian G. Gal. On the strong-to-strong interaction case for doubly nonlocal Cahn-Hilliard equations. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 131-167. doi: 10.3934/dcds.2017006

[9]

Ondrej Budáč, Michael Herrmann, Barbara Niethammer, Andrej Spielmann. On a model for mass aggregation with maximal size. Kinetic and Related Models, 2011, 4 (2) : 427-439. doi: 10.3934/krm.2011.4.427

[10]

Yanghong Huang, Andrea Bertozzi. Asymptotics of blowup solutions for the aggregation equation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1309-1331. doi: 10.3934/dcdsb.2012.17.1309

[11]

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

[12]

Olga Vasilyeva, Tamer Oraby, Frithjof Lutscher. Aggregation and environmental transmission in chronic wasting disease. Mathematical Biosciences & Engineering, 2015, 12 (1) : 209-231. doi: 10.3934/mbe.2015.12.209

[13]

Manuela Caratozzolo, Santina Carnazza, Luigi Fortuna, Mattia Frasca, Salvatore Guglielmino, Giovanni Gurrieri, Giovanni Marletta. Self-organizing models of bacterial aggregation states. Mathematical Biosciences & Engineering, 2008, 5 (1) : 75-83. doi: 10.3934/mbe.2008.5.75

[14]

R. Kowalczyk, A. Gamba, L. Preziosi. On the stability of homogeneous solutions to some aggregation models. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 203-220. doi: 10.3934/dcdsb.2004.4.203

[15]

Vincent Calvez, Gaël Raoul, Christian Schmeiser. Confinement by biased velocity jumps: Aggregation of escherichia coli. Kinetic and Related Models, 2015, 8 (4) : 651-666. doi: 10.3934/krm.2015.8.651

[16]

Miguel A. Herrero, Leandro Sastre. Models of aggregation in dictyostelium discoideum: On the track of spiral waves. Networks and Heterogeneous Media, 2006, 1 (2) : 241-258. doi: 10.3934/nhm.2006.1.241

[17]

Hyungjun Choi, Seung-Yeal Ha, Hansol Park. Emergent behaviors of discrete Lohe aggregation flows. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2021308

[18]

Karl Peter Hadeler, Shigui Ruan. Interaction of diffusion and delay. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 95-105. doi: 10.3934/dcdsb.2007.8.95

[19]

Justin Holmer, Maciej Zworski. Slow soliton interaction with delta impurities. Journal of Modern Dynamics, 2007, 1 (4) : 689-718. doi: 10.3934/jmd.2007.1.689

[20]

Jingzhen Liu, Yike Wang, Ming Zhou. Utility maximization with habit formation of interaction. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1451-1469. doi: 10.3934/jimo.2020029

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (263)
  • HTML views (0)
  • Cited by (36)

Other articles
by authors

[Back to Top]