<p>We explore the asymptotic analysis for a thermo-electroelastic problem in a 3-dimensional thin domain <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3113_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega ^\varepsilon $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Ω</mi> <mi>ε</mi> </msup> </math></EquationSource> </InlineEquation> with Coulomb’s boundary condition, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3113_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega ^\varepsilon $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Ω</mi> <mi>ε</mi> </msup> </math></EquationSource> </InlineEquation> is perturbed by a small parameter <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3113_Article_IEq3.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$\varepsilon >0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>></mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. The main contribution is twofold: (1) we derive the weak variational formulation and prove the unique solvability of the problem, and (2) we perform its asymptotic analysis as <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3113_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$\varepsilon \rightarrow 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, deriving and establishing the existence and uniqueness of a solution to the limiting problem.</p>

Three-dimensional asymptotic analysis of a bilateral contact problem in thermo-electro-elastic materials under Coulomb’s law

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发表日期：

2025年1月31日

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Zakaria Faiz,
Jinxia Cen,
Hicham Benaissa

摘要

We explore the asymptotic analysis for a thermo-electroelastic problem in a 3-dimensional thin domain $\Omega ^\varepsilon $ $Ω^{ε}$ with Coulomb’s boundary condition, where $\Omega ^\varepsilon $ $Ω^{ε}$ is perturbed by a small parameter $\varepsilon >0$ $ε > 0$ . The main contribution is twofold: (1) we derive the weak variational formulation and prove the unique solvability of the problem, and (2) we perform its asymptotic analysis as $\varepsilon \rightarrow 0$ $ε \to 0$ , deriving and establishing the existence and uniqueness of a solution to the limiting problem.