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References from Singular chemotaxis model unveiled: novel steady states and nonlinear stability in bounded domains. Local targets link to admitted publications; unresolved targets remain external evidence.
Bacterial chemotaxis in linear and nonlinear steady microfluidic gradients
10.1021/nl101204e · 2010 · External reference
Global well-posedness and asymptotic stabilization for chemotaxis system with signal-dependent sensitivity
10.1016/j.jde.2018.11.015 · 2019 · External reference
Global well-posedness of logarithmic Keller-Segel type systems
10.1016/j.jde.2021.03.053 · 2021 · External reference
The Weber-Fechner law: a misnomer that persists but that should go away
10.1037/rev0000278 · 2021 · External reference
Long-term monitoring of bacteria undergoing programmed population control in a microchemostat
10.1126/science.1109173 · 2005 · External reference
Stationary solutions with vacuum for a one-dimensional chemotaxis model with non-linear pressure
10.4310/cms.2016.v14.n1.a6 · 2015 · External reference
Phase transitions and bump solutions of the Keller-Segel model with volume exclusion
10.1137/19m125827x · 2020 · External reference
Boundary spike-layer solutions of the singular Keller-Segel system: existence and stability
10.1112/plms.12319 · 2021 · External reference
Boundary spike-layer solutions of the multi-dimensional singular Keller-Segel system: existence, profiles and stability
10.1112/plms.70122 · 2026 · External reference
Nonlinear stability of planar traveling waves in a chemotaxis model of tumor angiogenesis with chemical diffusion
10.1016/j.jde.2019.09.061 · 2020 · External reference
Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain
10.1016/j.jde.2018.02.034 · 2018 · External reference
Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model
10.1142/s0218202520500104 · 2020 · External reference
Well-posedness of a 3D parabolic-hyperbolic Keller-Segel system in the Sobolev space framework
10.1016/j.jde.2014.05.014 · 2014 · External reference
Mathematical analysis of a model for the initiation of angiogenesis
10.1137/s0036141001385046 · 2002 · External reference
Dynamical behavior of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions
10.1017/s0956792524000329 · 2025 · External reference
Percolation, morphogenesis and Burgers dynamics in blood vessels formation
10.1103/physrevlett.90.118101 · 2003 · External reference
A microfluidic chemostat for experiments with bacterial and yeast cells
10.1038/nmeth784 · 2005 · External reference
Global solutions to a hyperbolic-parabolic coupled system with large initial data
10.1016/s0252-9602(09)60059-x · 2009 · External reference
Stationary solutions with vacuum for a hyperbolic-parabolic chemotaxis model in dimension two
10.1016/j.nonrwa.2025.104489 · 2026 · External reference
Convergence of boundary layers for the Keller-Segel system with singular sensitivity in the half-plane
10.1016/j.matpur.2019.01.008 · 2019 · External reference
Stability of boundary layers for a viscous hyperbolic system arising from chemotaxis: one dimensional case
10.1137/17m112748x · 2018 · External reference
Boundary layer problem on a hyperbolic system arising from chemotaxis
10.1016/j.jde.2016.07.018 · 2016 · External reference
On a repulsion Keller-Segel system with a logarithmic sensitivity
10.1017/s0956792520000443 · 2022 · External reference
Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity
10.1016/j.jde.2013.04.002 · 2013 · External reference
Traveling bands of chemotactic bacteria: a theoretical analysis
10.1016/0022-5193(71)90051-8 · 1971 · External reference
A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data
10.1007/s00030-017-0472-8 · 2017 · External reference
Geometry effects on the boundary-layer profiles of the Keller-Segel system
10.1090/tran/9528 · 2025 · External reference
A system of reaction diffusion equations arising in the theory of reinforced random walks
10.1137/s0036139995291106 · 1997 · External reference
A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I: the role of protease inhibitors
10.1016/s0025-5564(00)00034-1 · 2000 · External reference
On a hyperbolic-parabolic system modeling chemotaxis
10.1142/s0218202511005519 · 2011 · External reference
Quantitative decay of a one-dimensional hybrid chemotaxis model with large data
10.1088/0951-7715/28/7/2181 · 2015 · External reference
Initial-boundary value problems for a system of hyperbolic balance laws arising from chemotaxis
10.1016/j.jde.2014.09.014 · 2015 · External reference
Stability of traveling waves of the Keller-Segel system with logarithmic sensitivity
10.1142/s0218202514500389 · 2014 · External reference
Global dynamics of a hyperbolic-parabolic model arising from chemotaxis
10.1137/110829453 · 2012 · External reference
Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions
10.4310/cms.2021.v19.n1.a10 · 2021 · External reference
Nonlinear stability of traveling waves to a hyperbolic-parabolic system modeling chemotaxis
10.1137/09075161x · 2009 · External reference
Nonlinear stability of large amplitude viscous shock waves of a generalized hyperbolic-parabolic system arising in chemotaxis
10.1142/s0218202510004830 · 2010 · External reference
Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
10.1016/j.jde.2010.09.020 · 2011 · External reference
Steadily propagating waves of a chemotaxis model
10.1016/j.mbs.2012.07.003 · 2012 · External reference
Asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology
10.1512/iumj.2018.67.7394 · 2018 · External reference
Aggregation, blowup and collapse: the ABC’s of taxis in reinforced random walks
10.1137/s0036139995288976 · 1997 · External reference
Nonlinear stability of strong traveling waves for the singular Keller-Segel system with large perturbations
10.1016/j.jde.2018.04.041 · 2018 · External reference
Boundary layers and stabilization of the singular Keller-Segel model
10.3934/krm.2018042 · 2018 · External reference
Global well-posedness and zero diffusion limit of classical solutions to 3D conservation laws arising in chemotaxis
10.1007/s00033-013-0378-1 · 2014 · External reference
On a hyperbolic-parabolic chemotaxis system
10.3934/mbe.2023337 · 2023 · External reference
Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions
10.3934/dcds.2019154 · 2019 · External reference
Generation of stable concentration gradients in 2D and 3D environments using a microfluidic ladder chamber
10.1007/s10544-007-9051-9 · 2007 · External reference
Convergence rate of solutions towards spiky steady state for the singular Keller-Segel system
10.1016/j.na.2023.113284 · 2023 · External reference
Global weak solutions in a chemotaxis system with large singular sensitivity
10.1016/j.nonrwa.2011.07.006 · 2011 · External reference
Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension
10.3934/dcdsb.2013.18.821 · 2013 · External reference
Cauchy problem of a system of parabolic conservation laws arising from the singular Keller-Segel model in multi-dimensions
10.1512/iumj.2021.70.8075 · 2021 · External reference
Global solutions of a Keller-Segel system with saturated logarithmic sensitivity function
10.3934/cpaa.2015.14.383 · 2015 · External reference
Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
10.1016/j.jde.2015.09.063 · 2016 · External reference
Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model
10.3934/cpaa.2013.12.3027 · 2013 · External reference
The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties
10.1142/s0218202516500238 · 2016 · External reference
Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption
10.1016/j.jde.2017.10.029 · 2018 · External reference
Stabilization in the logarithmic Keller-Segel system
10.1016/j.na.2018.01.002 · 2018 · External reference
Global existence of solutions to a hyperbolic-parabolic system
10.1090/s0002-9939-06-08773-9 · 2006 · External reference
Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity
10.1016/j.jmaa.2018.08.001 · 2018 · External reference
A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data
10.1007/s00030-017-0472-8 · ExternalCitation · doi-reference
Global well-posedness and zero diffusion limit of classical solutions to 3D conservation laws arising in chemotaxis
10.1007/s00033-013-0378-1 · ExternalCitation · doi-reference
Generation of stable concentration gradients in 2D and 3D environments using a microfluidic ladder chamber
10.1007/s10544-007-9051-9 · ExternalCitation · doi-reference
Traveling bands of chemotactic bacteria: a theoretical analysis
10.1016/0022-5193(71)90051-8 · ExternalCitation · doi-reference
Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
10.1016/j.jde.2010.09.020 · ExternalCitation · doi-reference
Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity
10.1016/j.jde.2013.04.002 · ExternalCitation · doi-reference
Well-posedness of a 3D parabolic-hyperbolic Keller-Segel system in the Sobolev space framework
10.1016/j.jde.2014.05.014 · ExternalCitation · doi-reference
Initial-boundary value problems for a system of hyperbolic balance laws arising from chemotaxis
10.1016/j.jde.2014.09.014 · ExternalCitation · doi-reference
Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis
10.1016/j.jde.2015.09.063 · ExternalCitation · doi-reference
Boundary layer problem on a hyperbolic system arising from chemotaxis
10.1016/j.jde.2016.07.018 · ExternalCitation · doi-reference
Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption
10.1016/j.jde.2017.10.029 · ExternalCitation · doi-reference
Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain
10.1016/j.jde.2018.02.034 · ExternalCitation · doi-reference
Nonlinear stability of strong traveling waves for the singular Keller-Segel system with large perturbations
10.1016/j.jde.2018.04.041 · ExternalCitation · doi-reference
Global well-posedness and asymptotic stabilization for chemotaxis system with signal-dependent sensitivity
10.1016/j.jde.2018.11.015 · ExternalCitation · doi-reference
Nonlinear stability of planar traveling waves in a chemotaxis model of tumor angiogenesis with chemical diffusion
10.1016/j.jde.2019.09.061 · ExternalCitation · doi-reference
Global well-posedness of logarithmic Keller-Segel type systems
10.1016/j.jde.2021.03.053 · ExternalCitation · doi-reference
Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity
10.1016/j.jmaa.2018.08.001 · ExternalCitation · doi-reference
Convergence of boundary layers for the Keller-Segel system with singular sensitivity in the half-plane
10.1016/j.matpur.2019.01.008 · ExternalCitation · doi-reference
Steadily propagating waves of a chemotaxis model
10.1016/j.mbs.2012.07.003 · ExternalCitation · doi-reference
Stabilization in the logarithmic Keller-Segel system
10.1016/j.na.2018.01.002 · ExternalCitation · doi-reference
Convergence rate of solutions towards spiky steady state for the singular Keller-Segel system
10.1016/j.na.2023.113284 · ExternalCitation · doi-reference
Global weak solutions in a chemotaxis system with large singular sensitivity
10.1016/j.nonrwa.2011.07.006 · ExternalCitation · doi-reference
Stationary solutions with vacuum for a hyperbolic-parabolic chemotaxis model in dimension two
10.1016/j.nonrwa.2025.104489 · ExternalCitation · doi-reference
A mathematical model for the roles of pericytes and macrophages in the initiation of angiogenesis. I: the role of protease inhibitors
10.1016/s0025-5564(00)00034-1 · ExternalCitation · doi-reference
Global solutions to a hyperbolic-parabolic coupled system with large initial data
10.1016/s0252-9602(09)60059-x · ExternalCitation · doi-reference
On a repulsion Keller-Segel system with a logarithmic sensitivity
10.1017/s0956792520000443 · ExternalCitation · doi-reference
Dynamical behavior of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions
10.1017/s0956792524000329 · ExternalCitation · doi-reference
Bacterial chemotaxis in linear and nonlinear steady microfluidic gradients
10.1021/nl101204e · ExternalCitation · doi-reference
The Weber-Fechner law: a misnomer that persists but that should go away
10.1037/rev0000278 · ExternalCitation · doi-reference
A microfluidic chemostat for experiments with bacterial and yeast cells
10.1038/nmeth784 · ExternalCitation · doi-reference
Quantitative decay of a one-dimensional hybrid chemotaxis model with large data
10.1088/0951-7715/28/7/2181 · ExternalCitation · doi-reference
Global existence of solutions to a hyperbolic-parabolic system
10.1090/s0002-9939-06-08773-9 · ExternalCitation · doi-reference
Geometry effects on the boundary-layer profiles of the Keller-Segel system
10.1090/tran/9528 · ExternalCitation · doi-reference
Percolation, morphogenesis and Burgers dynamics in blood vessels formation
10.1103/physrevlett.90.118101 · ExternalCitation · doi-reference
Boundary spike-layer solutions of the singular Keller-Segel system: existence and stability
10.1112/plms.12319 · ExternalCitation · doi-reference
Boundary spike-layer solutions of the multi-dimensional singular Keller-Segel system: existence, profiles and stability
10.1112/plms.70122 · ExternalCitation · doi-reference
Long-term monitoring of bacteria undergoing programmed population control in a microchemostat
10.1126/science.1109173 · ExternalCitation · doi-reference
Nonlinear stability of traveling waves to a hyperbolic-parabolic system modeling chemotaxis
10.1137/09075161x · ExternalCitation · doi-reference
Global dynamics of a hyperbolic-parabolic model arising from chemotaxis
10.1137/110829453 · ExternalCitation · doi-reference
Stability of boundary layers for a viscous hyperbolic system arising from chemotaxis: one dimensional case
10.1137/17m112748x · ExternalCitation · doi-reference
Phase transitions and bump solutions of the Keller-Segel model with volume exclusion
10.1137/19m125827x · ExternalCitation · doi-reference
Aggregation, blowup and collapse: the ABC’s of taxis in reinforced random walks
10.1137/s0036139995288976 · ExternalCitation · doi-reference
A system of reaction diffusion equations arising in the theory of reinforced random walks
10.1137/s0036139995291106 · ExternalCitation · doi-reference
Mathematical analysis of a model for the initiation of angiogenesis
10.1137/s0036141001385046 · ExternalCitation · doi-reference
Nonlinear stability of large amplitude viscous shock waves of a generalized hyperbolic-parabolic system arising in chemotaxis
10.1142/s0218202510004830 · ExternalCitation · doi-reference
On a hyperbolic-parabolic system modeling chemotaxis
10.1142/s0218202511005519 · ExternalCitation · doi-reference
Stability of traveling waves of the Keller-Segel system with logarithmic sensitivity
10.1142/s0218202514500389 · ExternalCitation · doi-reference
The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties
10.1142/s0218202516500238 · ExternalCitation · doi-reference
Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model
10.1142/s0218202520500104 · ExternalCitation · doi-reference
Asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology
10.1512/iumj.2018.67.7394 · ExternalCitation · doi-reference
Cauchy problem of a system of parabolic conservation laws arising from the singular Keller-Segel model in multi-dimensions
10.1512/iumj.2021.70.8075 · ExternalCitation · doi-reference
Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model
10.3934/cpaa.2013.12.3027 · ExternalCitation · doi-reference
Global solutions of a Keller-Segel system with saturated logarithmic sensitivity function
10.3934/cpaa.2015.14.383 · ExternalCitation · doi-reference
Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions
10.3934/dcds.2019154 · ExternalCitation · doi-reference
Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension
10.3934/dcdsb.2013.18.821 · ExternalCitation · doi-reference
Boundary layers and stabilization of the singular Keller-Segel model
10.3934/krm.2018042 · ExternalCitation · doi-reference
On a hyperbolic-parabolic chemotaxis system
10.3934/mbe.2023337 · ExternalCitation · doi-reference
Stationary solutions with vacuum for a one-dimensional chemotaxis model with non-linear pressure
10.4310/cms.2016.v14.n1.a6 · ExternalCitation · doi-reference
Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions
10.4310/cms.2021.v19.n1.a10 · ExternalCitation · doi-reference
