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arXiv · 2510.20642

Rothe's method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation

Karel Van Bockstal·Khonatbek Khompysh·Arshyn Altybay
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Abstract

In this paper, we investigate the inverse problem of determining an unknown time-dependent source term in a semilinear pseudo-parabolic equation with variable coefficients and a Dirichlet boundary condition. The unknown source term is recovered from additional measurement data expressed as a weighted spatial average of the solution. By employing Rothe's time-discretisation method, we prove the existence and uniqueness of a weak solution under a smallness condition on the problem data. We also provide a numerical scheme based on a perturbation approach, which reduces the solution of the resulting discrete problem to solving two standard variational problems and evaluating a scalar coefficient, and we demonstrate its accuracy and stability through numerical experiments.

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Karel Van Bockstal, Khonatbek Khompysh, Arshyn Altybay. 2025-10-23. Rothe's method in direct and time-dependent inverse source problems for a semilinear pseudo-parabolic equation. https://arxiv.org/abs/2510.20642

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