Inverse moving source problems for the wave equation
The inverse moving source problem of three-dimensional wave equation is investigated,and F(x,t)= f(x-a(t))g(t)is the moving source term.The Dirichlet data of the wave field in the measurement sphere is known,then by using the Fourier transform,the problem of wave equation can be transformed into the Helmholtz equation on frequency-domain,which enables us to establish the integral equality of the source term and the observation data.Based on the inverse Fourier transform as well as the existence and uniqueness theorem of first-order ODE,the existence and uniqueness of orbit function a(t)is demonstrated.Finally,by the integral inequality,the stability can be proved.
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