| Title:
|
Entropy of scalar reaction-diffusion equations (English) |
| Author:
|
Slijepčević, Siniša |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
139 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
597-605 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider scalar reaction-diffusion equations on bounded and extended domains, both with the autonomous and time-periodic nonlinear term. We discuss the meaning and implications of the ergodic Poincaré-Bendixson theorem to dynamics. In particular, we show that in the extended autonomous case, the space-time topological entropy is zero. Furthermore, we characterize in the extended nonautonomous case the space-time topological and metric entropies as entropies of a pair of commuting planar homeomorphisms. (English) |
| Keyword:
|
reaction-diffusion equation |
| Keyword:
|
attractor |
| Keyword:
|
invariant measure |
| Keyword:
|
entropy |
| Keyword:
|
Poincaré-Bendixson theorem |
| MSC:
|
35B40 |
| MSC:
|
37A35 |
| MSC:
|
37B40 |
| MSC:
|
37L30 |
| idZBL:
|
Zbl 06433684 |
| idMR:
|
MR3306850 |
| DOI:
|
10.21136/MB.2014.144137 |
| . |
| Date available:
|
2015-02-04T09:13:49Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144137 |
| . |
| Reference:
|
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| . |
