This article is cited in 1 paper

Differentical equations, dynamical systems and optimal control

On methods to solve an inverse problems for a nonlinear differential equation

E. V. Tabarintseva

South Urfal State University, pr. Lenina, 76, 454080, Chelyabinsk, Russia

Abstract: 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.

Keywords: operator equation, reverse time problem, regularization, error estimate.

UDC: 517.9

MSC: 35R25, 47J06

Received June 17, 2016, published March 14, 2017

DOI: 10.17377/semi.2017.14.020