A logarithmic chemotaxis model featuring global existence and aggregation

DOI10.1016/j.nonrwa.2019.05.010zbMath1430.92014OpenAlexW2951366252WikidataQ127637013 ScholiaQ127637013MaRDI QIDQ2286670

Changwook Yoon, Ariane Trescases, Laurent Desvillettes, Yong-Jung Kim

Publication date: 22 January 2020

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2019.05.010

zbMATH Keywords

pattern formationcross-diffusionKeller-Segel equationsduality lemmaasymmetric diffusioncell-aggregation

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Fokker-Planck equations (35Q84)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Starvation driven diffusion as a survival strategy of biological organisms
• Boundedness in a fully parabolic chemotaxis system with singular sensitivity
• Global weak solutions in a chemotaxis system with large singular sensitivity
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• A user's guide to PDE models for chemotaxis
• Large amplitude stationary solutions to a chemotaxis system
• Locating the peaks of least-energy solutions to a semilinear Neumann problem
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Global existence and aggregation in a Keller-Segel model with Fokker-Planck diffusion
• Parabolic system of chemotaxis: Blowup in a finite and the infinite time.
• Boundary spikes of a Keller-Segel chemotaxis system with saturated logarithmic sensitivity
• Bacterial chemotaxis without gradient-sensing
• Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
• A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data
• Blow-up in a chemotaxis model without symmetry assumptions
• A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity
• Improved Duality Estimates and Applications to Reaction-Diffusion Equations
• Global solutions in a fully parabolic chemotaxis system with singular sensitivity
• Chemotactic Traveling Waves by Metric of Food
• On the Entropic Structure of Reaction-Cross Diffusion Systems
• On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type
• On the shape of least‐energy solutions to a semilinear Neumann problem
• Blowup in Reaction-Diffusion Systems with Dissipation Of Mass
• A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system
• Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains
• The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results.

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