Levine, Howard A.; Sleeman, Brian D. A system of reaction diffusion equations arising in the theory of reinforced random walks. (English) Zbl 0874.35047 SIAM J. Appl. Math. 57, No. 3, 683-730 (1997). 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. Cited in 7 ReviewsCited in 118 Documents 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 Keywords:chemotaxis; reaction-diffusion systems; reinforced random walks; finite-time blow-up; collapse; aggregation PDFBibTeX XMLCite \textit{H. A. Levine} and \textit{B. D. Sleeman}, SIAM J. Appl. Math. 57, No. 3, 683--730 (1997; Zbl 0874.35047) Full Text: DOI