TY - JOUR
T1 - Global Solvability for a Nonlinear Semi-static Maxwell's Equation
AU - Hongming Yin  & Guofu Lu 
JO - Journal of Partial Differential Equations
VL - 2
SP - 113
EP - 125
PY - 2006
DA - 2006/05
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5323.html
KW - Nonlinear Maxwell's Equations
KW - Bean-like critical-state model
KW - Global existence and uniqueness
AB - <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>