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A mathematical model for the spread of morphogens with density dependent chemosensitivity

Publication ,  Journal Article
Merkin, JH; Needham, DJ; Sleeman, BD
Published in: Nonlinearity (UK)
2005

A system of reaction-diffusion equations with volume-filling chemosensitivity arising in the modelling of morphogen spread during embryonic growth is considered. Existence and uniqueness of classical solutions to this novel system are established. Qualitative behaviour, including similarity structure of solutions, is developed. The existence of weak solutions in certain situations is established and periodic pulse solutions are obtained numerically. The biological interpretation of the results is discussed

Duke Scholars

Published In

Nonlinearity (UK)

DOI

Publication Date

2005

Volume

18

Issue

6

Start / End Page

2745 / 2773

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Merkin, J. H., Needham, D. J., & Sleeman, B. D. (2005). A mathematical model for the spread of morphogens with density dependent chemosensitivity. Nonlinearity (UK), 18(6), 2745–2773. https://doi.org/10.1088/0951-7715/18/6/018
Merkin, J. H., D. J. Needham, and B. D. Sleeman. “A mathematical model for the spread of morphogens with density dependent chemosensitivity.” Nonlinearity (UK) 18, no. 6 (2005): 2745–73. https://doi.org/10.1088/0951-7715/18/6/018.
Merkin JH, Needham DJ, Sleeman BD. A mathematical model for the spread of morphogens with density dependent chemosensitivity. Nonlinearity (UK). 2005;18(6):2745–73.
Merkin, J. H., et al. “A mathematical model for the spread of morphogens with density dependent chemosensitivity.” Nonlinearity (UK), vol. 18, no. 6, 2005, pp. 2745–73. Manual, doi:10.1088/0951-7715/18/6/018.
Merkin JH, Needham DJ, Sleeman BD. A mathematical model for the spread of morphogens with density dependent chemosensitivity. Nonlinearity (UK). 2005;18(6):2745–2773.

Published In

Nonlinearity (UK)

DOI

Publication Date

2005

Volume

18

Issue

6

Start / End Page

2745 / 2773

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics