J H Merkin et al 2005 Nonlinearity 18 2745 doi:10.1088/0951-7715/18/6/018
J H Merkin1,3, D J Needham2 and B D Sleeman1
Show affiliationsRecommended by J A Glazier
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.
02.30.Jr Partial differential equations
35K57 Reaction-diffusion equations
92B05 General biology and biomathematics
Issue 6 (November 2005)
Received 29 March 2005
Published 3 October 2005
J H Merkin et al 2005 Nonlinearity 18 2745
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