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

J H Merkin et al 2005 Nonlinearity 18 2745-2773   doi: 10.1088/0951-7715/18/6/018  Help

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J H Merkin1,3, D J Needham2 and B D Sleeman1
1 Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK
2 Department of Mathematics, University of Reading, Reading RG6 6AX, UK
3 Author to whom any correspondence should be addressed.
E-mail: amtjhm@amsta.leeds.ac.uk

Recommended by J A Glazier

Abstract. 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.

Mathematics Subject Classification: 92B05, 92D15, 35K55, 35K57

Print publication: Issue 6 (November 2005)
Received 29 March 2005
Published 3 October 2005

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