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Unique Determination of Sound Speeds for Coupled Systems of Semi-linear Wave Equations
We consider coupled systems of semi-linear wave equations with different
sound speeds on a finite time interval and a bounded Lipschitz domain
in , with boundary . We show the coupled
systems are well posed for variable coefficient sounds speeds and short times.
Under the assumption of small initial data, we prove the source to solutions
map on associated with the nonlinear problem is
sufficient to determine the source-to-solution map for the linear problem. We
can then reconstruct the sound speeds in for the coupled nonlinear
wave equations under certain geometric assumptions. In the case of the full
source to solution map in this reconstruction could also be
accomplished under fewer geometric assumptions.Comment: minor update
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