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

Hongming Yin & Guofu Lu

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

Published online: 2006-05

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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.

  • Keywords

Nonlinear Maxwell's Equations Bean-like critical-state model Global existence and uniqueness

  • AMS Subject Headings

35Q60.

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5323.html} }
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 -

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.

Hongming Yin and Guofu Lu . (2006). Global Solvability for a Nonlinear Semi-static Maxwell's Equation. Journal of Partial Differential Equations. 19 (2). 113-125. doi:
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