Year: 2026
Type: preprint
Abstract: We consider a inverse problem for a hyperbolic equation. The objective is to simultaneous recover both the spatially varying coefficient, whose square root represents the wave speed, and the initial displacement from a single pair of Dirichlet-Neumann Cauchy data. By introducing a suitable transformation and differentiating the resulting equation in time, we derive a coupled system for the differences of the unknown coefficient and initial displacement. Combining weighted energy estimates with Carleman estimates, we establish a Lipschitz stability estimate for both unknown quantities in appropriate Sobolev norms. The proof relies on a priori regularity assumptions, non-degeneracy conditions on the initial data, and structural inequalities controlling the interaction between the coefficient and initial-displacement differences. Our result extends coefficient-only stability results to a simultaneous coefficient--initial-displacement identification problem.
Source: arXiv (Cornell University)
Authors: Ma, Shiqi, Zhai, Qi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7471714805
OpenAlex ID: W7214590569