Name
Abstract | ||
|---|---|---|
This paper proves that ordinary differential equation systems that are contractive with respect to Lp norms remain so when diffusion is added. Thus, diffusive instabilities, in the sense of the Turing phenomenon, cannot arise for such systems, and in fact any two solutions converge exponentially to each other. The key tools are semi inner products and logarithmic Lipschitz constants in Banach spaces. An example from biochemistry is discussed, which shows the necessity of considering non-Hilbert spaces. An analogous result for graph-defined interconnections of systems defined by ordinary differential equations is given as well. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.na.2013.01.001 | Nonlinear Analysis: Theory, Methods & Applications |
Keywords | Field | DocType |
Logarithmic norm,Logarithmic Lipschitz constant,Reaction diffusion PDEs,Diffusive instability,Turing phenomenon | Mathematical optimization,Ordinary differential equation,Mathematical analysis,Instability,Banach space,Lipschitz continuity,Turing,Logarithmic norm,Logarithm,Mathematics,Exponential growth | Journal |
Volume | ISSN | Citations |
83 | 0362-546X | 6 |
PageRank | References | Authors |
0.52 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zahra Aminzare | 1 | 17 | 3.58 |
| Eduardo D. Sontag | 2 | 3134 | 781.88 |