Higher dimensional inverse problem of the wave equation for a general multi-connected bounded domain with a finite number of smooth mixed boundary conditions

摘要

The spectral function μ(t)=∑J=1∞exp(−itμJ1/2) where {μJ}J=1∞ are the eigenvalues of the negative Laplacian −Δ3=−∑υ=13(∂/∂xυ)2 in the (x1,x2,x3)-space, is studied for small |t| for a variety of bounded domains, where −∞