Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production

DOI10.4171/JEMS/749zbMath1406.35068arXiv1608.07622OpenAlexW2963543811MaRDI QIDQ1687383

Michael Winkler, Youshan Tao

Publication date: 29 December 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.07622

zbMATH Keywords

infinite time blow-up

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44) Comparison principles in context of PDEs (35B51)

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Cites Work

• Pattern formation in a model for mountain pine beetle dispersal: linking model predictions to data
• On a multiscale model involving cell contractivity and its effects on tumor invasion
• Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
• Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis
• Initiation of slime mold aggregation viewed as an instability
• A Lyapunov function for a two-chemical species version of the chemotaxis model
• Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity
• A user's guide to PDE models for chemotaxis
• Continuous and discrete mathematical models of tumor-induced angiogenesis
• Pattern formation in generalized Turing systems. I: Steady-state patterns in systems with mixed boundary conditions
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Development and applications of a model for cellular response to multiple chemotactic cues
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• The basin of attraction of the steady-states for a chemotaxis model in \(\mathbb R^2\) with critical mass
• Overview of mathematical approaches used to model bacterial chemotaxis. II: Bacterial popu\-lations
• Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• Blow-up in a chemotaxis model without symmetry assumptions
• Bacterial swimming and oxygen transport near contact lines
• Boundedness and stabilization in a multi-dimensional chemotaxis—haptotaxis model
• Analysis of a Mathematical Model of Ischemic Cutaneous Wounds
• ASYMPTOTIC BEHAVIOR OF GLOBAL SOLUTIONS TO A MODEL OF CELL INVASION
• Finite-time blow-up in a quasilinear system of chemotaxis
• On Explosions of Solutions to a System of Partial Differential Equations Modelling Chemotaxis
• Mathematical Analysis of a Model for the Initiation of Angiogenesis
• Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
• MATHEMATICAL MODELLING OF CANCER CELL INVASION OF TISSUE: THE ROLE OF THE UROKINASE PLASMINOGEN ACTIVATION SYSTEM
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item