Blow-up dynamics for the aggregation equation with degenerate diffusion
From MaRDI portal
Publication:2443090
DOI10.1016/j.physd.2013.01.009zbMath1286.35050OpenAlexW2134370460MaRDI QIDQ2443090
Publication date: 4 April 2014
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2013.01.009
Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic equations (35K15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Blow-up in context of PDEs (35B44) Self-similar solutions to PDEs (35C06) Integro-partial differential equations (35R09) Axially symmetric solutions to PDEs (35B07)
Related Items
Convergence of Regularized Nonlocal Interaction Energies, Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent \(m > 0\), Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems, Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits, A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker-Planck equation, Cops on the dots in a mathematical model of urban crime and police response, Global existence versus blow-up in a high dimensional Keller-Segel equation with degenerate diffusion and nonlocal aggregation, A blob method for the aggregation equation, Aggregation-diffusion to constrained interaction: minimizers \& gradient flows in the slow diffusion limit, On a chemotaxis model with degenerate diffusion: initial shrinking, eventual smoothness and expanding, Partial regularity and blow-up asymptotics of weak solutions to degenerate parabolic systems of porous medium type
Uses Software
Cites Work
- Unnamed Item
- Asymptotics of blowup solutions for the aggregation equation
- Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems.
- Fully discrete analysis of a discontinuous finite element method for the keller-segel chemotaxis model
- Chemotactic collapse for the Keller-Segel model
- Precise computations of chemotactic collapse using moving mesh methods
- Nonlinear porous medium flow with fractional potential pressure
- Notes on finite difference schemes to a parabolic-elliptic system modelling chemotaxis
- Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
- From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
- Optimal critical mass in the two dimensional Keller-Segel model in \(R^2\)
- Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
- Stochastic particle approximation for measure valued solutions of the 2D Keller-Segel system
- Critical chemotactic collapse
- A finite volume scheme for the Patlak-Keller-Segel chemotaxis model
- Discontinuous Galerkin methods for the chemotaxis and haptotaxis models
- Global Existence and Finite Time Blow-Up for Critical Patlak--Keller--Segel Models with Inhomogeneous Diffusion
- Virial theorem and dynamical evolution of self-gravitating Brownian particles in an unbounded domain. I. Overdamped models
- The Patlak–Keller–Segel Model and Its Variations: Properties of Solutions via Maximum Principle
- Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion
- Grow-Up Rate and Refined Asymptotics for a Two-Dimensional Patlak–Keller–Segel Model in a Disk
- Conservative upwind finite-element method for a simplified Keller–Segel system modelling chemotaxis
- Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2
- Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
- Convergence of the Mass-Transport Steepest Descent Scheme for the Subcritical Patlak–Keller–Segel Model
- Asymptotically self‐similar blow‐up of semilinear heat equations
- Diffusion, attraction and collapse
- Self-similar solutions of the second kind for the modified porous medium equation
- Symmetric Singularity Formation in Lubrication-Type Equations for Interface Motion
- A study of blow-ups in the Keller–Segel model of chemotaxis
- New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model
- Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$
- Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
- Self-similar solutions of the second kind in nonlinear filtration
