Journal or Book Title
SIAM Journal on Applied Mathematics
We investigate the properties of solutions of a system of chemotaxis equations arising in the theory of reinforced random walks. We show that under some circumstances, finite-time blow-up of solutions is possible. In other circumstances, the solutions will decay to a spatially constant solution (collapse). We also give some intuitive arguments which demonstrate the possibility of the existence of aggregation (piecewise constant) solutions.
Society for Industrial and Applied Mathematics
Levine, Howard A. and Sleeman, Brian D., "A System of Reaction Diffusion Equations Arising in the Theory of Reinforced Random Walks" (1997). Mathematics Publications. 50.