On the Cauchy Problem for the Wave Equation with Data on the Boundary

详细

The Cauchy problem for the wave equation in Ω × ℝ with data given on some part of the boundary ∂Ω × ℝ is considered. A reconstruction algorithm for this problem based on analytic expressions is given. This result is applicable to the problem of determining a nonstationary wave field arising in geophysics, photoacoustic tomography, tsunami wave source recovery.