Detecting a hidden obstacle via the time domain enclosure method. A scalar wave case

Masaru Ikehata

Published 2017-09-07Version 1

The characterization problem of the existence of an unknown obstacle behind a known obstacle is considered by using a singe observed wave at a place where the wave is generated. The unknown obstacle is invisible from the place by using visible ray. A mathematical formulation of the problem using the classical wave equation is given. The main result consists of two parts: (i) one can make a decision whether the unknown obstacle exists or not behind a known impenetrable obstacle by using a single wave over a finte time interval under some a-priori information on the position of the unknown obstacle; (ii) one can obtain a lower bound of the Euclidean distance of the unknown obstacle to the center point of the support of the intial data of the wave. The proof is a combination of the time domain enclosure method and some previous results on the Gaussian lower estimates for the heat kernels.