Abstract:
The solvability of the inverse problem of finding a
solution problem $u(x,t)$ and the unknown coefficients
$q_{1}(t),\ldots,q_{m}(t)$ in the many-dimensional hyperbolic
equation when setting the conditions for initial boundary value
problem and the conditions of the overdetermination. Existence of
solutions are proven.
Keywords:inverse problem, conditions of
redefinition, hyperbolic equation, wave equation, a priori estimate.