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@unpublished{faucris.269652687,
abstract = {In this paper, we study the problem of initial data identification for weak-entropy solutions
of 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
identification problem under consideration ill-posed. To get around this issue, we introduce
a non-smooth optimization 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
L2(R) norm. Here, we characterize the set of minimizers of the aforementioned non-smooth
optimization problem. One of the minimizers is the backward entropy solution, constructed
using a backward forward method. Some simulations are given using a wave-front tracking
algorithm.