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<p>This paper investigates the inverse Cauchy problem for nonlinear parabolic partial differential equations. We begin by studying the well-posedness of the associated boundary value problem (BVP). To address the intrinsic ill-posedness of the inverse problem, we reformulate it as a least-squares minimization problem, adding a vanishing regularization term. Numerical experiments conducted in both stationary and time-dependent regimes demonstrate the robustness of the proposed method to noise, its fast convergence, and its improved accuracy compared to the gradient descent method with a fixed step.</p>

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Reconstruction of missing boundary data for nonlinear parabolic systems using a control-type approach

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Marwa Ouni,
  • Anis Bel Hadj Hassin

摘要

This paper investigates the inverse Cauchy problem for nonlinear parabolic partial differential equations. We begin by studying the well-posedness of the associated boundary value problem (BVP). To address the intrinsic ill-posedness of the inverse problem, we reformulate it as a least-squares minimization problem, adding a vanishing regularization term. Numerical experiments conducted in both stationary and time-dependent regimes demonstrate the robustness of the proposed method to noise, its fast convergence, and its improved accuracy compared to the gradient descent method with a fixed step.