| Title:
|
A note on the Cahn-Hilliard equation in $H^1(\mathbb R^N)$ involving critical exponent (English) |
| Author:
|
Cholewa, Jan W. |
| Author:
|
Rodriguez-Bernal, Anibal |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
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0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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139 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
269-283 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the Cahn-Hilliard equation in $H^1(\mathbb R^N)$ with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as $|u|\to \infty $ and logistic type nonlinearities. In both situations we prove the $H^2(\mathbb R^N)$-bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012). (English) |
| Keyword:
|
initial value problem for higher order parabolic equations |
| Keyword:
|
asymptotic behavior of solutions |
| Keyword:
|
critical exponent |
| MSC:
|
35B33 |
| MSC:
|
35B40 |
| MSC:
|
35K30 |
| MSC:
|
35K59 |
| idZBL:
|
Zbl 06362258 |
| idMR:
|
MR3238839 |
| DOI:
|
10.21136/MB.2014.143854 |
| . |
| Date available:
|
2014-07-14T08:27:43Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143854 |
| . |
| Reference:
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