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@article{faucris.306948338,
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 nonsmooth 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 L^{2}(ℝ) norm. Here, we characterize the set of minimizers of the aforementioned nonsmooth 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.},
author = {Liard, Thibault and Zuazua Iriondo, Enrique},
doi = {10.1137/22M1478720},
faupublication = {yes},
journal = {SIAM Journal on Mathematical Analysis},
keywords = {backward-forward method; conservation laws; identification problems; nonsmooth optimization problem; wave-front tracking algorithm; weak-entropy solutions},
note = {CRIS-Team Scopus Importer:2023-06-30},
pages = {1949-1968},
peerreviewed = {Yes},
title = {{ANALYSIS} {AND} {NUMERICAL} {SOLVABILITY} {OF} {BACKWARD}-{FORWARD} {CONSERVATION} {LAWS}},
volume = {55},
year = {2023}
}