A system of reaction diffusion equations arising in the theory of reinforced random walks. (English) Zbl 0874.35047
Summary: 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.
MSC:
35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
35M10 | PDEs of mixed type |
35R25 | Ill-posed problems for PDEs |