Boundedness for a fully parabolic Keller-Segel model with sublinear segregation and superlinear aggregation

DOI10.1007/s10440-021-00386-6zbMath1469.35111arXiv2005.08064OpenAlexW3128605208MaRDI QIDQ2040616

Silvia Frassu, Giuseppe Viglialoro

Publication date: 14 July 2021

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.08064

zbMATH Keywords

global existencenonlinear productionzero-flux problem

Mathematics Subject Classification ID

Cell movement (chemotaxis, etc.) (92C17) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (17)

Existence of almost periodic solution for nonlocal fractional Cauchy problem with integral initial condition ⋮ Investigation on dynamics of an impulsive predator-prey system with generalized Holling type IV functional response and anti-predator behavior ⋮ Some new oscillation criteria of fourth-order quasi-linear differential equations with neutral term ⋮ Hyers-Ulam stability of non-autonomous and nonsingular delay difference equations ⋮ On the oscillations of the solutions for a class of second order nonlinear functional dynamic equations on time scales with unbounded neutral coefficients ⋮ A nonlinear attraction-repulsion Keller-Segel model with double sublinear absorptions: criteria toward boundedness ⋮ Properties of given and detected unbounded solutions to a class of chemotaxis models ⋮ Global solution of the chemotaxis attraction-repulsion Cauchy problem with the nonlinear signal production in \(\mathbb{R}^N\) ⋮ A linearized decoupled Crank-Nicolson FEM for Keller-Segel chemotactic model with nonlinear secretion ⋮ Blow-up phenomena in a parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with superlinear logistic degradation ⋮ Unnamed Item ⋮ Remarks on two connected papers about Keller-Segel systems with nonlinear production ⋮ Boundedness in a nonlinear attraction-repulsion Keller-Segel system with production and consumption ⋮ Finite-time blow-up in a quasilinear degenerate parabolic-elliptic chemotaxis system with logistic source and nonlinear production ⋮ Blow-up prevention by logistic source an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction ⋮ An efficient numerical simulation and mathematical modeling for the prevention of tuberculosis ⋮ Global existence of solutions to a two-species predator–prey parabolic chemotaxis system

Cites Work

• Unnamed Item
• Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity
• Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
• Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• A user's guide to PDE models for chemotaxis
• Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
• Pattern formation in a generalized chemotactic model
• Mathematical biology. Vol. 1: An introduction.
• Global existence of solutions to an \(n\)-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth and superlinear production
• Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension
• Global in time and bounded solutions to a parabolic-elliptic chemotaxis system with nonlinear diffusion and signal-dependent sensitivity
• New critical exponents in a fully parabolic quasilinear Keller-Segel system and applications to volume filling models
• A refined criterion and lower bounds for the blow-up time in a parabolic-elliptic chemotaxis system with nonlinear diffusion
• Boundedness in logistic Keller-Segel models with nonlinear diffusion and sensitivity functions
• Boundedness in a chemotaxis system with nonlinear signal production
• Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains
• Boundedness vs. blow-up in a chemotaxis system
• Boundedness in a chemotaxis–haptotaxis model with nonlinear diffusion
• Does a ‘volume-filling effect’ always prevent chemotactic collapse?
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• On a Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions
• Boundedness in a fully parabolic chemotaxis‐consumption system with nonlinear diffusion and sensitivity, and logistic source
• A critical blow-up exponent in a chemotaxis system with nonlinear signal production
• Solvability of a Keller–Segel system with signal-dependent sensitivity and essentially sublinear production
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

This page was built for publication: Boundedness for a fully parabolic Keller-Segel model with sublinear segregation and superlinear aggregation