LARGE-TIME BEHAVIOR OF A PARABOLIC-PARABOLIC CHEMOTAXIS MODEL WITH LOGARITHMIC SENSITIVITY IN ONE DIMENSION

No abstract is available for this paper.

• Publication year

  2012

• Venue

  Discrete and Continuous Dynamical Systems-series B

• Publication date

  2012-12-01

• Fields of study

  Mathematics

• Identifiers
  DOI 10.3934/DCDSB.2013.18.821
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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  1999cited by this paper
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  1995cited by this paper
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  1991cited by this paper
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  1988cited by this paper
• LP Bounds of solutions of reaction-diffusion equations

  1979influential reference
• Elliptic Partial Differential Equa-tions of Second Order

  1977cited by this paper
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  1971cited by this paper
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  year unknowncited by this paper

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