publications by David Needham.

Papers Published

1. Merkin, J.H. and Needham, D.J. and Sleeman, B.D., A mathematical model for the spread of morphogens with density dependent chemosensitivity, Nonlinearity (UK), vol. 18 no. 6 (2005), pp. 2745 - 73 [018] .
   (last updated on 2007/04/06)

   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

   Keywords:
   biochemistry;biodiffusion;cellular biophysics;physiological models;reaction-diffusion systems;