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<p>This study concerns third-order partial differential equations (PDEs) with non-local integral and non-classical boundary conditions. The primary focus is on establishing the well-posedness of the associated non-local boundary value problem (BVP). Using an operator-based method, we derive stability theorems that guarantee the continuous dependence of the solution on the input data. We then apply these stability theorems to obtain explicit stability estimates for two specific non-local boundary value problems involving third-order PDEs, thereby demonstrating the practical implications of our theoretical results.</p>

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STABILITY ANALYSIS OF THIRD-ORDER PARTIAL DIFFERENTIAL EQUATION UNDER SPECIFIC NONCLASSICAL INTEGRAL CONDITIONS

  • 期刊论文

  • 发表日期：

    2026年1月31日

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  • Allaberen Ashyralyev,
  • Kheireddine Belakroum,
  • Mossaab Hebik

摘要

This study concerns third-order partial differential equations (PDEs) with non-local integral and non-classical boundary conditions. The primary focus is on establishing the well-posedness of the associated non-local boundary value problem (BVP). Using an operator-based method, we derive stability theorems that guarantee the continuous dependence of the solution on the input data. We then apply these stability theorems to obtain explicit stability estimates for two specific non-local boundary value problems involving third-order PDEs, thereby demonstrating the practical implications of our theoretical results.