| Title:
|
Cross-Diffusion Systems with Entropy Structure (English) |
| Author:
|
Jüngel, Ansgar |
| Language:
|
English |
| Journal:
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Proceedings of Equadiff 14 |
| Volume:
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Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017 |
| Issue:
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2017 |
| Year:
|
|
| Pages:
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181-190 |
| . |
| Category:
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math |
| . |
| Summary:
|
Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems by Lepoutre, Moussa, and co-workers for cross-diffusion systems with an additional Laplace structure. The boundedness-by-entropy method allows for global bounded weak solutions to certain diffusion systems. Furthermore, a partial result on the uniqueness of weak solutions is recalled, and some open problems are presented. (English) |
| Keyword:
|
Strongly coupled parabolic systems, local existence of solutions, global existence of solutions, gradient flow, duality method, boundedness-by-entropy method, nonlinear Aubin-Lions lemma, Kullback-Leibler entropy |
| MSC:
|
35B65 |
| MSC:
|
35K51 |
| MSC:
|
35K57 |
| . |
| Date available:
|
2019-09-27T07:55:45Z |
| Last updated:
|
2019-09-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/703046 |
| . |
| Reference:
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