Stable determination of damping and potential coefficients in a semilinear wave equation

RESUMO

We consider an inverse problem for a semilinear wave equation with time-independent damping, linear potential, and nonlinear potential coefficients in a bounded domain of $\mathbb{R}^n$ for $n\geq 2$. The main objective is to establish stability estimates for the simultaneous recovery of these coefficients from the associated Dirichlet-to-Neumann map. Our approach combines second-order linearization with suitably constructed geometric optics and asymptotic solutions. We establish Hölder-type stability estimates for the recovery of each of the three coefficients appearing in the semilinear wave equation under suitable a priori bounds on these coefficients. To the best of our knowledge, this is the first stability result for simultaneous determination of time-independent damping, linear and nonlinear potentials in a semiliner wave equation.