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
APA
Chicago
ICMJE
MLA
NLM
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