Direct and inverse problem for bi-wave equation with time-dependent coefficients from partial data

Sombuddha Bhattacharyya; Pranav Kumar

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arXiv · 2504.15911

Direct and inverse problem for bi-wave equation with time-dependent coefficients from partial data

Sombuddha Bhattacharyya·Pranav Kumar

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Abstract

In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and boundary data in suitable function spaces. In the inverse problem, we prove uniqueness of the lower order time-dependent perturbations from the partial input-output operator. The restriction in the measurements are considered by restricting some of the Neumann data over a portion of the lateral boundary.

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Sombuddha Bhattacharyya, Pranav Kumar. 2025-04-22. Direct and inverse problem for bi-wave equation with time-dependent coefficients from partial data. https://arxiv.org/abs/2504.15911

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