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<p>The aim of this paper is to study the local existence of solutions to an abstract quasilinear coupled system of Kirchhoff and heat equations with a nonlinear inhomogeneous term. We establish local existence using a method introduced by Kato [<CitationRef CitationID="CR22">22</CitationRef>], combined with the multiplier method and a fixed-point argument.</p>

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Existence results for an abstract coupled Kirchhoff-heat system with source terms

  • 期刊论文

  • 发表日期：

    2026年5月30日

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  • Mohamed Hocine Braiki,
  • Zakaria Chedjara,
  • Abdelhamid Hallouz,
  • Svetlin Georgiev Georgiev

摘要

The aim of this paper is to study the local existence of solutions to an abstract quasilinear coupled system of Kirchhoff and heat equations with a nonlinear inhomogeneous term. We establish local existence using a method introduced by Kato [22], combined with the multiplier method and a fixed-point argument.