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<p>In the present paper, we consider a porous thermoelastic system with a single dissipation mechanism generated by thermal damping. The heat flux introduced in the system is modeled by the Gurtin–Pipkin thermal law. By utilizing a semigroup approach and the Hille-Yosida theorem, we establish the existence of a unique solution. In addition, we introduce a stability number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\chi _g\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>χ</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> that depends on the coefficients of the system and establish an exponential stability result, provided that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\chi _g=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>χ</mi> <mi>g</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. Otherwise, if <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\chi _g\ne 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>χ</mi> <mi>g</mi> </msub> <mo>≠</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, we prove the absence of exponential decay. Our result improves and generalizes the previous results in the literature obtained for Fourier’s and Cattaneo’s laws of thermal conductivity.</p>

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On the time behavior of a porous thermoelastic system with only thermal dissipation given by Gurtin–Pipkin law

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Afaf Ahmima,
  • Abdelfeteh Fareh

摘要

In the present paper, we consider a porous thermoelastic system with a single dissipation mechanism generated by thermal damping. The heat flux introduced in the system is modeled by the Gurtin–Pipkin thermal law. By utilizing a semigroup approach and the Hille-Yosida theorem, we establish the existence of a unique solution. In addition, we introduce a stability number \(\chi _g\) χ g that depends on the coefficients of the system and establish an exponential stability result, provided that \(\chi _g=0\) χ g = 0 . Otherwise, if \(\chi _g\ne 0\) χ g ≠ 0 , we prove the absence of exponential decay. Our result improves and generalizes the previous results in the literature obtained for Fourier’s and Cattaneo’s laws of thermal conductivity.