Singular patterns in Keller–Segel-type models

Variational methods applied to PDEs (35A15) Degenerate parabolic equations (35K65) Cell movement (chemotaxis, etc.) (92C17) Second-order parabolic systems (35K40) Traveling wave solutions (35C07) Soliton solutions (35C08) Quasilinear parabolic equations (35K59)

Cites Work

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Qualitative behavior and traveling waves for flux-saturated porous media equations arising in optimal mass transportation
On a chemotaxis model with saturated chemotactic flux
Qualitative behaviour for flux-saturated mechanisms: travelling waves, waiting time and smoothing effects
On the entropy conditions for some flux limited diffusion equations
An existence and uniqueness result for flux limited diffusion equations
Pattern formation in a flux limited reaction-diffusion equation of porous media type
The two-dimensional Keller-Segel model after blow-up
Traveling bands of chemotactic bacteria: a theoretical analysis
Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
Complexity and mathematical tools toward the modelling of multicellular growing systems
A user's guide to PDE models for chemotaxis
Pairings between measures and bounded functions and compensated compactness
Optimal critical mass in the two dimensional Keller-Segel model in \(R^2\)
Kinetic models for chemotaxis and their drift-diffusion limits
On the analysis of traveling waves to a nonlinear flux limited reaction-diffusion equation
Flux-saturated porous media equations and applications
The Cauchy problem for a strongly degenerate quasilinear equation
Flux limited generalized porous media diffusion equations
The Diffusion Limit of Transport Equations II: Chemotaxis Equations
On the relativistic heat equation in one space dimension
Radially Symmetric Solutions of a Tempered Diffusion Equation. A Porous Media, Flux-Limited Case
Random walk with persistence and external bias
Convergence of flux limited porous media diffusion equations to its classical counterpart
A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up
WAVES FOR A HYPERBOLIC KELLER–SEGEL MODEL AND BRANCHING INSTABILITIES
QUALITATIVE PROPERTIES OF THE SOLUTIONS OF A NONLINEAR FLUX-LIMITED EQUATION ARISING IN THE TRANSPORT OF MORPHOGENS
The one-dimensional chemotaxis model: global existence and asymptotic profile
The one-dimensional Keller–Segel model with fractional diffusion of cells
MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS
Formation of discontinuities in flux-saturated degenerate parabolic equations
Cross-diffusion and traveling waves in porous-media flux-saturated Keller–Segel models
Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision
Finite Speed of Propagation and Waiting Time Phenomena for Degenerate Parabolic Equations with Linear Growth Lagrangian
Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
Finite-time blow-up in a degenerate chemotaxis system with flux limitation
MULTICELLULAR BIOLOGICAL GROWING SYSTEMS: HYPERBOLIC LIMITS TOWARDS MACROSCOPIC DESCRIPTION
On reaction processes with saturating diffusion
MODEL HIERARCHIES FOR CELL AGGREGATION BY CHEMOTAXIS

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