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Determining a nonlinear hyperbolic system with unknown sources and nonlinearity

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arxiv 2107.10219 v2 pith:Q7SMQGGZ submitted 2021-07-21 math.AP

Yi-Hsuan Lin , Hongyu Liu , Xu Liu This is my paper
classification math.AP
keywords nonlinearitysourceshyperbolicboundaryequationinitialordersemilinear
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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.

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