| Title:
|
Porous medium equation and fast diffusion equation as gradient systems (English) |
| Author:
|
Littig, Samuel |
| Author:
|
Voigt, Jürgen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
869-889 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that the Porous Medium Equation and the Fast Diffusion Equation, $\dot u-\Delta u^m=f$, with $m\in (0,\infty )$, can be modeled as a gradient system in the Hilbert space $H^{-1}(\Omega )$, and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets $\Omega \subseteq \mathbb R^n$ and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions. (English) |
| Keyword:
|
porous medium equation |
| Keyword:
|
gradient system |
| Keyword:
|
fast diffusion |
| Keyword:
|
asymptotic behaviour |
| Keyword:
|
order preservation |
| MSC:
|
34G20 |
| MSC:
|
35G25 |
| MSC:
|
47H99 |
| MSC:
|
47J35 |
| idZBL:
|
Zbl 06537697 |
| idMR:
|
MR3441322 |
| DOI:
|
10.1007/s10587-015-0214-1 |
| . |
| Date available:
|
2016-01-13T09:01:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144779 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
|
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| . |
