Article
MSC:
35A15,
35D30,
47H05,
65N30,
78M10,
78M30 | MR 4444786 | Zbl 07584079 | DOI: 10.21136/AM.2021.0365-20
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Keywords:
well-posedness; uniform monotonicity; S-property; $p$-curl systems
well-posedness; uniform monotonicity; S-property; $p$-curl systems
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.
References:
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