Stationary Ring and Concentric-Ring Solutions of the Keller--Segel Model with Quadratic Diffusion
From MaRDI portal
Publication:5124645
DOI10.1137/19M1298998zbMath1454.35027arXiv1911.02193OpenAlexW3088915544MaRDI QIDQ5124645
Publication date: 30 September 2020
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1911.02193
Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Bifurcations in context of PDEs (35B32) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)
Related Items
Stability, free energy and dynamics of multi-spikes in the minimal Keller-Segel model, The existence and stability of spikes in the one-dimensional Keller-Segel model with logistic growth
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Qualitative analysis of stationary Keller-Segel chemotaxis models with logistic growth
- Uniqueness for Keller-Segel-type chemotaxis models
- Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent \(m > 0\)
- Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
- Stationary states of quadratic diffusion equations with long-range attraction
- On a chemotaxis model with saturated chemotactic flux
- Bubbling on boundary submanifolds for the Lin-Ni-Takagi problem at higher critical exponents
- Dynamics of spike in a Keller-Segel's minimal chemotaxis model
- The volcano effect in bacterial chemotaxis
- Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
- Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data
- On the boundary spike layer solutions to a singularly perturbed Neumann problem
- Chemotactic collapse for the Keller-Segel model
- Stability of spiky solution of Keller-Segel's minimal chemotaxis model
- Initiation of slime mold aggregation viewed as an instability
- Model for chemotaxis
- Traveling bands of chemotactic bacteria: a theoretical analysis
- Stationary solutions with vacuum for a one-dimensional chemotaxis model with nonlinear pressure
- The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
- Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
- A user's guide to PDE models for chemotaxis
- On global bifurcation for quasilinear elliptic systems on bounded domains
- Large amplitude stationary solutions to a chemotaxis system
- Nonlinear aspects of chemotaxis
- Degree theory for \(C^1\) Fredholm mappings of index 0
- A non-local model for a swarm
- Locating the peaks of least-energy solutions to a semilinear Neumann problem
- Spiky steady states of a chemotaxis system with singular sensitivity
- Congested aggregation via Newtonian interaction
- Ground states in the diffusion-dominated regime
- Multipeak solutions for a semilinear Neumann problem
- Multiple interior peak solutions for some singularly perturbed Neumann problems.
- Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
- Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly's compactness theorem
- Convergence to equilibria of global solutions to a degenerate quasilinear Keller-Segel system
- Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus
- On a chemotaxis model with degenerate diffusion: initial shrinking, eventual smoothness and expanding
- Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics
- Existence of compactly supported global minimisers for the interaction energy
- Equilibria of homogeneous functionals in the fair-competition regime
- Time-periodic and stable patterns of a two-competing-species Keller-Segel chemotaxis model: effect of cellular growth
- Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
- Boundedness vs. blow-up in a chemotaxis system
- Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term
- Global existence and steady states of a two competing species Keller-Segel chemotaxis model
- Some global results for nonlinear eigenvalue problems
- Bifurcation from simple eigenvalues
- The Parabolic-Parabolic Keller-Segel System with Critical Diffusion as a Gradient Flow in ℝd,d ≥ 3
- An Aggregation Equation with Degenerate Diffusion: Qualitative Property of Solutions
- The Patlak–Keller–Segel Model and Its Variations: Properties of Solutions via Maximum Principle
- Stationary States of an Aggregation Equation with Degenerate Diffusion and Bounded Attractive Potential
- A Primer of Swarm Equilibria
- Compactly supported stationary states of the degenerate Keller-Segel system in the diffusion-dominated regime
- On the number of interior peak solutions for a singularly perturbed Neumann problem
- A hybrid variational principle for the Keller–Segel system in ℝ2
- Does a ‘volume-filling effect’ always prevent chemotactic collapse?
- Stationary Solutions of Chemotaxis Systems
- On the shape of least‐energy solutions to a semilinear Neumann problem
- The Variational Formulation of the Fokker--Planck Equation
- Computation of Modified Bessel Functions and Their Ratios
- Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
- High-energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponents
- Qualitative Behavior of Solutions of Chemotactic Diffusion Systems: Effects of Motility and Chemotaxis and Dynamics
- Aggregation-Diffusion Equations: Dynamics, Asymptotics, and Singular Limits
- Phase Transitions and Bump Solutions of the Keller--Segel Model with Volume Exclusion
- Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction
