The paper is devoted to the finding of the coefficient of one nonlinear wave equation in the mixed problem. The considered problem is reduced to the optimal control problem with proper functional. Differentiability of functional is proved and the necessary optimality conditions are derived in the form of the variational inequality. Existence of the optimal control is proved.

Detonation of explosives creates strong para-seismic vibrations. Such vibrations can damage buildings or other infrastructure located in the vicinity of such detonations, and can be burdensome to people living in such areas. This paper describes the usefulness of Matching Pursuit (MP) algorithm in assessing the impact of blasting on the surrounding areas, and proves that by taking into account frequency changes over time, vibration analysis can help make much more profound and reliable predictions in this field.