| Title:
|
Convergence estimate for second order Cauchy problems with a small parameter (English) |
| Author:
|
Najman, Branko |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
737-745 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter $\varepsilon .$ The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem. (English) |
| MSC:
|
34E15 |
| MSC:
|
34G20 |
| MSC:
|
35B25 |
| MSC:
|
35R15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0952.35151 |
| idMR:
|
MR1658257 |
| . |
| Date available:
|
2009-09-24T10:17:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127451 |
| . |
| Reference:
|
[1] Engel, K.-J.: On singular perturbations of second order Cauchy problems.Pac. J. Math. 152 (1992), 79–91. Zbl 0743.34063, MR 1139973, 10.2140/pjm.1992.152.79 |
| Reference:
|
[2] Fattorini, H.O.: Second Order Linear Differential Equations in Banach Spaces.North Holland, 1985. Zbl 0564.34063, MR 0797071 |
| Reference:
|
[3] Najman, B.: Time singular limit of semilinear wave equations with damping.J. Math. Anal. Appl. 174 (1991), 95–117. MR 1212920, 10.1006/jmaa.1993.1104 |
| . |
