@Article{JPDE-19-113,
author = {Hongming Yin  and Guofu Lu },
title = {Global Solvability for a Nonlinear Semi-static Maxwell's Equation},
journal = {Journal of Partial Differential Equations},
year = {2006},
volume = {19},
number = {2},
pages = {113--125},
abstract = {<p>In this paper we study a nonlinear Maxwell&#39;s system in a highly conductive medium in which the displacement current is neglected. The magnetic field H satisfies a quasilinear evolution system: H_t + ∇ × [r(x, t, |H|, |∇ × H|)∇ × H] = F(x, t,H), where the resistivity r is assumed to depend upon the strengths of electric and magnetic fields while the internal magnetic current F depends upon the magnetic field. It is shown that under appropriate structure conditions for r and F the above nonlinear system subject to appropriate initial-boundary conditions has a unique global solution.</p>},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5323.html}
}