| Title:
|
Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems (English) |
| Author:
|
Song, Chang-Ho |
| Author:
|
Ri, Yong-Gon |
| Author:
|
Sin, Cholmin |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
67 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
431-444 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation $Au=b$. We prove that if $A$ is a quasi-uniformly monotone and hemi-continuous operator, then $A^{-1}$ is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic $p$-curl systems. (English) |
| Keyword:
|
well-posedness |
| Keyword:
|
uniform monotonicity |
| Keyword:
|
S-property |
| Keyword:
|
$p$-curl systems |
| MSC:
|
35A15 |
| MSC:
|
35D30 |
| MSC:
|
47H05 |
| MSC:
|
65N30 |
| MSC:
|
78M10 |
| MSC:
|
78M30 |
| idZBL:
|
Zbl 07584079 |
| idMR:
|
MR4444786 |
| DOI:
|
10.21136/AM.2021.0365-20 |
| . |
| Date available:
|
2022-06-28T13:20:31Z |
| Last updated:
|
2024-09-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/150436 |
| . |
| Reference:
|
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| Reference:
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