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Abstract <p>A nonlinear problem formulated in a non-Lipschitz domain describing a pointwise contact of a nonhomogeneous <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2D\)</EquationSource> <!--LobJMat2561440Lazarev-m1--> </InlineEquation> body with a thin rigid inclusion is considered. The domain boundary has one single cusp. A non penetration condition subject to possible contact interaction is imposed at a vertex of the cusp. Using a fictitious domain method the existence of a solution is proved. An auxiliary problem is formulated in a wider domain. Moreover, it is shown that solutions of the auxiliary and initial problems coincides.</p>

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Fictitious Domain Method for a Point Contact Problem for a Nonhomogeneous Body with a Thin Rigid Inclusion

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • N. P. Lazarev,
  • E. D. Fedotov,
  • G. M. Semenova

摘要

Abstract

A nonlinear problem formulated in a non-Lipschitz domain describing a pointwise contact of a nonhomogeneous \(2D\) body with a thin rigid inclusion is considered. The domain boundary has one single cusp. A non penetration condition subject to possible contact interaction is imposed at a vertex of the cusp. Using a fictitious domain method the existence of a solution is proved. An auxiliary problem is formulated in a wider domain. Moreover, it is shown that solutions of the auxiliary and initial problems coincides.