Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems

Chang-Ho Song; Yong-Gon Ri; Cholmin Sin

Applications of Mathematics (2022)

  • Volume: 67, Issue: 4, page 431-444
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Song, Chang-Ho, Ri, Yong-Gon, and Sin, Cholmin. "Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems." Applications of Mathematics 67.4 (2022): 431-444. <http://eudml.org/doc/298314>.

@article{Song2022,
abstract = {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.},
author = {Song, Chang-Ho, Ri, Yong-Gon, Sin, Cholmin},
journal = {Applications of Mathematics},
language = {eng},
number = {4},
pages = {431-444},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text \{curl\}$ systems},
url = {http://eudml.org/doc/298314},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Song, Chang-Ho
AU - Ri, Yong-Gon
AU - Sin, Cholmin
TI - Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 431
EP - 444
AB - 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.
LA - eng
UR - http://eudml.org/doc/298314
ER -

References

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