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arXiv · 2509.24470

A Source Identification Problem for the Bi-Parabolic Equation Containing a Poly-harmonic Operator

Dang Duc Trong·Bui Thanh Duy·Nguyen Dang Minh
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Abstract

In this paper, we address the source identification problem for the bi-parabolic equation involving a operator. Specifically, we investigate the equation $(\partial_t +\frak A)^2u(t)=\psi(t)f$, where $\frak A$ denotes a poly-harmonic operator. Given the perturbed data of $\psi$ and $u(T)$ (where $T>0$), our objective is to determine $f$. Although several scientific publications have explored regularization techniques for bi-parabolic problems, the existing literature remains limited. By relaxing certain conditions on the function $\psi$ and employing a truncation regularization method while considering the problem on an unbounded domain, we believe our results provide valuable insights.

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Dang Duc Trong, Bui Thanh Duy, Nguyen Dang Minh. 2025-09-29. A Source Identification Problem for the Bi-Parabolic Equation Containing a Poly-harmonic Operator. https://arxiv.org/abs/2509.24470

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