The effects of cross-diffusion and logistic source on the boundedness of solutions to a pursuit-evasion model

Asymptotic behavior of solutions to PDEs (35B40) Cell movement (chemotaxis, etc.) (92C17) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51) Classical solutions to PDEs (35A09)

Cites Work

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Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source
A quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic type with logistic source
Analysis of kinetic and macroscopic models of pursuit-evasion dynamics
Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation
Initiation of slime mold aggregation viewed as an instability
Chemotaxis with logistic source: very weak global solutions and their boundedness properties
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect
From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
A blow-up result for a quasilinear chemotaxis system with logistic source in higher dimensions
Preventing blow up in a chemotaxis model
Semi-linear second-order elliptic equations in \(L^1\)
Parabolic system of chemotaxis: Blowup in a finite and the infinite time.
Global boundedness in a chemotaxis quasilinear parabolic predator-prey system with pursuit-evasion
Global boundedness and stability of solutions for prey-taxis model with handling and searching predators
Global solvability of prey-predator models with indirect predator-taxis
A blow-up result for attraction-repulsion system with nonlinear signal production and generalized logistic source
Large time behavior in a predator-prey system with pursuit-evasion interaction
Blow-up prevention by logistic source an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction
A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing
Boundedness and asymptotic behavior in a predator-prey model with indirect pursuit-evasion interaction
Large time behavior in a predator-prey system with indirect pursuit-evasion interaction
Boundedness and stabilization enforced by mild saturation of taxis in a producer-scrounger model
Boundedness in quasilinear Keller-Segel equations with nonlinear sensitivity and logistic source
The role of superlinear damping in the construction of solutions to drift-diffusion problems with initial data in \(L^{1}\)
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
Boundedness in a chemotaxis system with nonlinear signal production
On a quasilinear parabolic-elliptic chemotaxis system with logistic source
Predator-prey model with prey-taxis and diffusion
A chemotaxis predator-prey model with indirect pursuit-evasion dynamics and parabolic signal
A parabolic-quasilinear predator-prey model under pursuit-evasion dynamics
Blow-up in a chemotaxis model without symmetry assumptions
Predator–prey model with diffusion and indirect prey-taxis
Finite-time blow-up in a quasilinear system of chemotaxis
Does a ‘volume-filling effect’ always prevent chemotactic collapse?
Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis
A critical blow-up exponent in a chemotaxis system with nonlinear signal production
Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion
Existence Theory and Qualitative Analysis for a Fully Cross-Diffusive Predator-Prey System
A Chemotaxis System with Logistic Source
Boundedness in a quasilinear fully parabolic Keller-Segel system with logistic source
Long time behavior of the solution to a chemotaxis system with nonlinear indirect signal production and logistic source