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<p>In this work, we are interested in the existence of solutions for a nonlinear parabolic–elliptic coupled system in inhomogeneous anisotropic Orlicz–Sobolev spaces without assuming the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{\Delta _2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">Δ</mi> <mn mathvariant="bold">2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation><b>-condition</b> on the <i>N</i>-function. The system describes the heat generated within a semiconductor device by an electrical current. This may be seen as a generalization of the well-known thermistor problem. The main purpose of this paper is to prove two main results: the existence of a weak solution via Schauder’s fixed point theorem, and the existence of a capacity solution.</p>

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On the existence of capacity solution for a parabolic perturbed thermistor problem in Orlicz–Sobolev spaces

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Hakima Ouyahya,
  • Mohamed Rhoudaf,
  • Hajar Talbi

摘要

In this work, we are interested in the existence of solutions for a nonlinear parabolic–elliptic coupled system in inhomogeneous anisotropic Orlicz–Sobolev spaces without assuming the \(\varvec{\Delta _2}\) Δ 2 -condition on the N-function. The system describes the heat generated within a semiconductor device by an electrical current. This may be seen as a generalization of the well-known thermistor problem. The main purpose of this paper is to prove two main results: the existence of a weak solution via Schauder’s fixed point theorem, and the existence of a capacity solution.