Simultaneous Determination of Wave Speed, Diffusivity, and Nonlinearity in the Westervelt Equation Using Complex Time-Periodic Solutions
Abstract
Abstract. We consider an inverse problem governed by the Westervelt equation with linear diffusivity and quadratic-type nonlinearity. The objective of this problem is to recover all the coefficients of this nonlinear partial differential equation. We show that by constructing complex-valued time-periodic solutions excited from the boundary time-harmonically at a sufficiently high frequency, knowledge of the first- and second-harmonic Cauchy data at the boundary is sufficient to simultaneously determine the wave speed, diffusivity, and nonlinearity in the interior of the domain of interest.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Fractional Differential Equations Solutions
Numerical methods for differential equations
Publication details
- Journal / source
- SIAM Journal on Applied Mathematics
- Volume
- 86
- Issue
- 1
- Pages
- 1–20
- Publication date
- 6 January 2026
- Language
- EN