Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2022-06-28T13:20:31Z |
| Last updated: | 2022-12-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/150436 |
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