Determining a nonlinear hyperbolic system with unknown sources and nonlinearity

Abstract

We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic scenarios that one can uniquely determine the nonlinearity or the sources by using passive or active boundary observations. In order to exploit the nonlinearity and the sources simultaneously, we develop a new technique, which combines the observability for linear wave equations and a Runge approximation with higher order linearization for the semilinear hyperbolic equation.

arXiv comment31 pages. Some typos are corrected. All comments are welcome

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Cited by in corpus (4)

• Simultaneous recoveries for semilinear parabolic systems
• Simultaneous recovery of piecewise analytic coefficients in a semilinear elliptic equation
• Some integral geometry problems for wave equations
• An inverse problem for semilinear equations involving the fractional Laplacian