Analysis and numerical solvability of backward-forward conservation laws
Liard T, Zuazua Iriondo E (2024)
Publication Language: English
Publication Status: Accepted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2024
Publisher: SIAM Journal on Mathematical Analysis
URI: https://dcn.nat.fau.eu/wp-content/uploads/AnalysisNumSolvability_tLiardEZuazua.pdf
DOI: 10.1137/22m1478720
Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/AnalysisNumSolvability_tLiardEZuazua.pdf
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.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
France (FR)How to cite
APA:
Liard, T., & Zuazua Iriondo, E. (2024). Analysis and numerical solvability of backward-forward conservation laws. (Unpublished, Accepted).
MLA:
Liard, Thibault, and Enrique Zuazua Iriondo. Analysis and numerical solvability of backward-forward conservation laws. Unpublished, Accepted. 2024.
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