GLOBAL SOLVABILITY FOR A NONLINEAR SEMI-STATIC MAXWELL'S EQUATION

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Nonlinear Maxwell's Equations Bean-like critical-state model Global existence and uniqueness.
• 年，卷（期）: 2006,（2）
• 页码范围: 113-125
• 页数: 13页
• 分类号: O175.29
• 语种: 英文

摘要

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: Ht + ▽ × [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.