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

Laurent Desvillettes, Michèle Grillot, Philippe Grillot, Simona Mancini
2018 Discrete and Continuous Dynamical Systems. Series A  
In this paper we study a degenerate parabolic system of reactiondiffusion equations arising in cellular biology models. Its specificity lies in the fact that one of the concentrations does not diffuse. Under realistic conditions on the reaction term, we prove existence and uniqueness of a nonnegative solution to the considered system, and we study its regularity. Moreover, we discuss the existence and linear stability of the steady solutions (equilibria), and give a sufficient condition on the
more » ... eaction term for Turing-like instabilities to be triggered. These results are finally illustrated by some numerical simulations. 2010 Mathematics Subject Classification. Primary: 35K65, 82B21; Secondary: 35B35.
doi:10.3934/dcds.2018205 fatcat:vtkry6u5pbbatkwk5pm3fd7hz4