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In this paper we are interested in a degenerate parabolic system ofreaction-diffusion equations arising in biology when studying cell adhesion atthe protein level. In this modeling the unknown is the couple of thedistribution laws of the freely diffusing proteins and of the fixed ones. Undersufficient conditions on the aggregation and unbinding probabilities, we provethe existence of solution of the considered system, as well as theirpositivity, boundedness and uniqueness. Moreover, we discuss the stability ofthe equilibrium solution. Finally, we show that the simpler and particularchoice of an affine aggregation function and of a constant unbindingprobability do not lead to pattern formation as expected in the application.These analytical results are also supported by some numerical simulation.

Study of a degenerate reaction-diffusion system arising in particle dynamics with aggregation effects