A user’s guide to PDE models for chemotaxis

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Hillen, T., and K. J. Painter. “A user’s Guide to PDE Models for Chemotaxis”. Journal of Mathematical Biology, vol. 58, no. 1-2, 2008, pp. 183-17, https://doi.org/10.1007/s00285-008-0201-3.
Hillen, T., & Painter, K. J. (2008). A user’s guide to PDE models for chemotaxis. Journal of Mathematical Biology, 58(1-2), 183-217. https://doi.org/10.1007/s00285-008-0201-3
Hillen, T., and K. J. Painter. “A user’s Guide to PDE Models for Chemotaxis”. Journal of Mathematical Biology 58, no. 1-2 (2008): 183-217. https://doi.org/10.1007/s00285-008-0201-3.
Hillen T, Painter KJ. A user’s guide to PDE models for chemotaxis. Journal of Mathematical Biology. 2008;58(1-2):183-217.
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 12 2007
Global Attractors for Cross Diffusion Systems on Domains of Arbitrary Dimension Rocky Mountain Journal of Mathematics
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Free-flight responses ofDrosophila melanogasterto attractive odors

 Journal of Experimental Biology
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  • Science: Chemistry: Organic chemistry: Biochemistry
 143 2006
Refrences Analysis
Category Category Repetition
Science: Biology (General)96
Medicine: Medicine (General): Computer applications to medicine. Medical informatics31
Science: Chemistry: Organic chemistry: Biochemistry30
Science: Mathematics25
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods16
Science: Physics5
Science: Biology (General): Ecology5
Science: Biology (General): Genetics4
Science: Science (General)3
Science: Biology (General): Cytology3
Science: Biology (General): Evolution3
Medicine: Medicine (General)3
Technology: Environmental technology. Sanitary engineering2
Technology: Chemical technology: Chemical engineering2
Science: Mathematics: Instruments and machines: Electronic computers. Computer science1
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Medicine: Internal medicine: Neurosciences. Biological psychiatry. Neuropsychiatry: Neurology. Diseases of the nervous system1
Medicine: Internal medicine: Neurosciences. Biological psychiatry. Neuropsychiatry1
Technology: Chemical technology: Biotechnology1
Science: Microbiology1
Science: Chemistry1
Agriculture: Plant culture1
Agriculture: Animal culture1
The category Science: Biology (General) 96 is the most frequently represented among the references in this article. It primarily includes studies from Journal of Mathematical Biology and Journal of Theoretical Biology. The chart below illustrates the number of referenced publications per year.
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Citations
Title Journal Journal Categories Citations Publication Date
Effects of indirect signal absorption in the chemotaxis system involving singularly signal‐dependent motilities

 Mathematische Nachrichten
  • Science: Mathematics
 2024
Well‐posedness of diffusion–aggregation equations with bounded kernels and their mean‐field approximations

 Mathematical Methods in the Applied Sciences
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2024
Global weak solutions to a fully parabolic two‐species chemotaxis system with fast p$$ p $$‐Laplacian diffusion

 Mathematical Methods in the Applied Sciences
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2024
A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects

 Journal of Evolution Equations
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2024
Boundedness and large-time behavior in a chemotaxis system with signal-dependent motility arising from tumor invasion Zeitschrift für angewandte Mathematik und Physik
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
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Citations Analysis
Category Category Repetition
Science: Mathematics793
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods610
Science: Biology (General)108
Science: Physics87
Medicine: Medicine (General): Computer applications to medicine. Medical informatics85
Science: Chemistry: Organic chemistry: Biochemistry79
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Science: Science (General)35
Science: Physics: Electricity and magnetism: Electricity: Plasma physics. Ionized gases29
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Science: Chemistry: Physical and theoretical chemistry19
Technology: Mechanical engineering and machinery18
Science: Mathematics: Instruments and machines: Electronic computers. Computer science14
Science13
Medicine11
Technology: Environmental technology. Sanitary engineering10
Science: Biology (General): Ecology10
Science: Mathematics: Analysis9
Science: Chemistry8
Technology: Chemical technology7
Science: Biology (General): Genetics7
Technology: Electrical engineering. Electronics. Nuclear engineering: Materials of engineering and construction. Mechanics of materials6
Medicine: Medicine (General): Medical technology6
Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software5
Geography. Anthropology. Recreation: Environmental sciences4
Medicine: Medicine (General)3
Technology: Electrical engineering. Electronics. Nuclear engineering: Electric apparatus and materials. Electric circuits. Electric networks3
Science: Biology (General): Cytology3
Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics: Computer engineering. Computer hardware3
Science: Mathematics: Probabilities. Mathematical statistics3
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Medicine: Public aspects of medicine: Toxicology. Poisons1
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Science: Physics: Heat: Thermodynamics1
Science: Physics: Acoustics. Sound1
Science: Physics: Optics. Light1
Medicine: Medicine (General): Medical physics. Medical radiology. Nuclear medicine1
Technology: Chemical technology: Biotechnology1
The category Science: Mathematics 793 is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled Traveling wave solutions from microscopic to macroscopic chemotaxis models and was published in 2009. The most recent citation comes from a 2024 study titled Complete infinite-time mass aggregation in a quasilinear Keller–Segel system. This article reached its peak citation in 2022, with 118 citations. It has been cited in 233 different journals, 17% of which are open access. Among related journals, the Journal of Differential Equations cited this research the most, with 93 citations. The chart below illustrates the annual citation trends for this article.
Citations used this article by year