О решении одной обратной задачи для нелинейного дифференциального уравнения в классе кусочно-гладких функций

We study a reverse time problem for a nonlinear differential equation. The exact solution is given to be a piecewise smooth function. We suggest an approach for constructing a stable approximate solution to the inverse problem taking into account the a priori information about the exact solution. We obtain sharp error estimates for the approximate solutions.