Volume 19, Issue 2
Global Solvability for a Nonlinear Semi-static Maxwell's Equation

Hongming Yin and Guofu Lu

J. Part. Diff. Eq., 19 (2006), pp. 113-125.

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  • Abstract

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.

  • History

Published online: 2006-05

  • AMS Subject Headings

35Q60.

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