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<p>In this paper, we are concerned with the Landau-Lifshitz-Gilbert equation (LLG) in a new form proposed in [<CitationRef CitationID="CR32">32</CitationRef>] that describes magnetization dynamics of a ferromagnetic body including the role of conduction electrons spin. Considering the one dimensional case, we prove local existence in time and uniqueness of a regular solution with finite energy. The method relies on Galerkin approximating solutions and refined estimates which give rise to a solution of our problem during a time interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((0, T^\star )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <msup> <mi>T</mi> <mo>⋆</mo> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On a model of Landau-Lifshitz-Gilbert equation for conducting ferromagnets

  • 期刊论文

  • 发表日期：

    2025年12月23日

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  • Kamel Hamdache,
  • Djamila Hamroun

摘要

In this paper, we are concerned with the Landau-Lifshitz-Gilbert equation (LLG) in a new form proposed in [32] that describes magnetization dynamics of a ferromagnetic body including the role of conduction electrons spin. Considering the one dimensional case, we prove local existence in time and uniqueness of a regular solution with finite energy. The method relies on Galerkin approximating solutions and refined estimates which give rise to a solution of our problem during a time interval \((0, T^\star )\) ( 0 , T ⋆ ) .