Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn--Hilliard Approximation
DOI10.1137/15M1031151zbMath1351.35228arXiv1507.04259OpenAlexW2962985184WikidataQ58933865 ScholiaQ58933865MaRDI QIDQ2819090
Andrew J. Bernoff, Chad M. Topaz
Publication date: 28 September 2016
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1507.04259
Integro-partial differential equations (45K05) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Developmental biology, pattern formation (92C15) Animal behavior (92D50) Integro-partial differential equations (35R09)
Related Items (6)
Cites Work
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- A nonlocal continuum model for biological aggregation
- Asymptotics of blowup solutions for the aggregation equation
- Global attractor for a nonlocal model for biological aggregation
- Inhomogeneous Patlak-Keller-Segel models and aggregation equations with nonlinear diffusion in \(\mathbb{R}^d\)
- Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion
- The thin film equation with backwards second order diffusion
- Global minimizers for free energies of subcritical aggregation equations with degenerate diffusion
- Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions
- An integro-differential equation arising as a limit of individual cell-based models
- Higher order nonlinear degenerate parabolic equations
- The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels
- Finite-time blow-up of \(L^\infty \)-weak solutions of an aggregation equation
- On KS-type equations describing the evolution and rupture of a liquid interface
- Spatial coupling of plant and herbivore dynamics: The contribution of herbivore dispersal to transient and persistent ``waves of damage
- Mathematical biology. Vol. 1: An introduction.
- Mutual interactions, potentials, and individual distance in a social aggregation
- Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
- Existence of ground states of nonlocal-interaction energies
- Well-posedness theory for aggregation sheets
- A biharmonic-modified forward time stepping method for fourth order nonlinear diffusion equations
- Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
- Finite-time blow-up of solutions of an aggregation equation in \(\mathbb R^n\)
- An Aggregation Equation with Degenerate Diffusion: Qualitative Property of Solutions
- Nonlocal Aggregation Models: A Primer of Swarm Equilibria
- Stability and clustering of self-similar solutions of aggregation equations
- Stationary States and Asymptotic Behavior of Aggregation Models with Nonlinear Local Repulsion
- AGGREGATION AND SPREADING VIA THE NEWTONIAN POTENTIAL: THE DYNAMICS OF PATCH SOLUTIONS
- Characterization of Radially Symmetric Finite Time Blowup in Multidimensional Aggregation Equations
- Explicit flock solutions for Quasi-Morse potentials
- On global minimizers of repulsive–attractive power-law interaction energies
- A Primer of Swarm Equilibria
- Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion
- Lp theory for the multidimensional aggregation equation
- Swarm dynamics and equilibria for a nonlocal aggregation model
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- Long-wave instabilities and saturation in thin film equations
- Spinodal decomposition for the cahn-hilliard equation
- Thin Films with High Surface Tension
- Properties of steady states for thin film equations
- A diffuse interface approach to Hele Shaw flow
- Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
- Counting the stationary states of the Sivashinsky equation
- Counting stationary solutions of the Cahn–Hilliard equation by transversality arguments
- On the Cahn–Hilliard Equation with Degenerate Mobility
- Asymptotic Dynamics of Attractive-Repulsive Swarms
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Pattern formation outside of equilibrium
- A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
- Complex spatial group patterns result from different animal communication mechanisms
- Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$
- Derivation of macroscopic equations for individual cell‐based models: a formal approach
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