% Encoding: UTF-8
@COMMENT{BibTeX export based on data in FAU CRIS: https://cris.fau.de/}
@COMMENT{For any questions please write to cris-support@fau.de}
@misc{faucris.236488976,
abstract = {In this paper, we study the problem of inverse design for the one-dimensional Burgers equation. This problem consists in identifying the set of initial data evolving to a given target at a final time. Due to the time-irreversibility of the Burgers equation, some target functions are unattainable from solutions of this equation, making the inverse problem under consideration ill-posed. To get around this issue, we introduce an optimal control problem which consists in minimizing the difference between the predictions of the Burgers equation and the observations of the system at a final time in $L^2(R)$ norm. The two main contributions of this work are the following:- We fully characterize the set of minimizers of the aforementioned optimal control problem
- A wave-front tracking method is implemented to construct numerically all of them

One of minimizers is the backward entropy solution, constructed using a backward-forward metho},
author = {Liard, Thibault and Zuazua, Enrique},
faupublication = {yes},
keywords = {Inverse problems; Conservation Laws; Entropy solutions; Backward-Forward approach; Optimal Control Problem; Wave-front tracking algorithm.},
peerreviewed = {automatic},
title = {{Inverse} design for the one-dimensional {Burgers} equation},
year = {2019}
}