On a Hyperbolic Coefficient Inverse Problem via Partial Dynamic Boundary Measurements

[摘要] This paper is devoted to the identification of the unknown smooth coefficientcentering the hyperbolic equationc(x)∂t2u−Δu=0in a bounded smooth domain inℝdfrom partial (on part of the boundary) dynamic boundary measurements. In this paper, we provethat the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subsetΓof the boundary determines explicitly the coefficientcprovided thatcis known outside a bounded domain. Then, through constructionof appropriate test functions by a geometrical control method, we derive a formula for calculating the coefficientcfrom the knowledge of the difference between the local Dirichlet-to-Neumann maps.

[学科分类] 应用数学