TY - JOUR T1 - Global Solvability for a Nonlinear Semi-static Maxwell's Equation 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 -

In this paper we study a nonlinear Maxwell'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.