| Title:
|
Second order quasilinear functional evolution equations (English) |
| Author:
|
Simon, László |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
139-152 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in $(0,T)$ is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in $(0,\infty )$ (boundedness and stabilization as $t\to \infty $) are shown. (English) |
| Keyword:
|
functional evolution equation |
| Keyword:
|
second order quasilinear equation |
| Keyword:
|
monotone operator |
| MSC:
|
35A01 |
| MSC:
|
35A02 |
| MSC:
|
35B35 |
| MSC:
|
35R10 |
| MSC:
|
35R20 |
| idZBL:
|
Zbl 06486930 |
| idMR:
|
MR3368490 |
| DOI:
|
10.21136/MB.2015.144322 |
| . |
| Date available:
|
2015-06-30T12:13:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144322 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
