| Title:
|
Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions (English) |
| Author:
|
Ngoc, Le Thi Phuong |
| Author:
|
Long, Nguyen Thanh |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
165-196 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence, compactness techniques and the construction of a suitable Lyapunov functional. To our knowledge, there has been no decay or blow up result for equations of Love waves or Love type waves before. (English) |
| Keyword:
|
nonlinear Love equation |
| Keyword:
|
Faedo-Galerkin method |
| Keyword:
|
local existence |
| Keyword:
|
blow up |
| Keyword:
|
exponential decay |
| MSC:
|
35L20 |
| MSC:
|
35L70 |
| MSC:
|
35Q74 |
| MSC:
|
37B25 |
| idZBL:
|
Zbl 06562152 |
| idMR:
|
MR3470772 |
| DOI:
|
10.1007/s10492-016-0127-9 |
| . |
| Date available:
|
2016-03-17T19:32:32Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144843 |
| . |
| Reference:
|
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