Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements

2011/01/25 by Oksanen, Lauri
#35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.4836

Abstract

We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of \Rⁿ, and generalize the concept of \em domain of influence. We present an efficient minimization algorithm to compute the volume of a domain of influence using boundary measurements and time-reversed boundary measurements. Moreover, we show that if the manifold is simple, then the volumes of the domains of influence determine the manifold. For a continuous real valued function τ on the boundary of the manifold, the domain of influence is the set of those points on the manifold from which the travel time to some boundary point y is less than τ(y).

Related

• Inverse obstacle problem for the non-stationary wave equation with an unknown background
• On inverse problems for a strongly damped wave equation on compact manifolds
• An Inverse Problem for symmetric hyperbolic Partial Differential Operators on Complete Riemannian Manifolds
• Equivalence of time-domain inverse problems and boundary spectral problems
• Counterexamples to inverse problems for the wave equation