Large time behavior in a forager–exploiter model with different taxis strategies for two groups in search of food

DOI10.1142/S021820251950043XzbMath1425.35200MaRDI QIDQ4973273

Michael Winkler, Youshan Tao

Publication date: 3 December 2019

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

chemotaxisglobal existencelarge time behavior

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51)

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Cites Work

• Unnamed Item
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• Global bounded solutions of the higher-dimensional Keller-Segel system under smallness conditions in optimal spaces
• Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities
• Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant
• Global stability of prey-taxis systems
• Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
• The patch distributed producer-scrounger game
• Asymptotic homogenization in a three-dimensional nutrient taxis system involving food-supported proliferation
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• Stabilization in a two-dimensional chemotaxis-Navier-Stokes system
• Stabilization in a chemotaxis model for tumor invasion
• Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• The two-dimensional Keller–Segel system with singular sensitivity and signal absorption: Global large-data solutions and their relaxation properties
• ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS
• Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations
• Boundedness in chemotaxis systems with rotational flux terms
• Logarithmic Sobolev Inequalities
• Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives
• Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions
• Pattern formation in prey-taxis systems