2025/09/29 by Dang Duc Trong, Trong, Dang Duc, Bui Thanh Duy +3
Mathematics · Engineering · #Numerical methods in inverse problems #Differential Equations and Boundary Problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2509.24470
In this paper, we address the source identification problem for the bi-parabolic equation involving a operator. Specifically, we investigate the equation (∂t +\frak A)2u(t)=ψ(t)f, where \frak A denotes a poly-harmonic operator. Given the perturbed data of ψ 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 ψ and employing a truncation regularization method while considering the problem on an unbounded domain, we believe our results provide valuable insights.