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Publication Type: Unpublished / Preprint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. 

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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 (Unpublished, Accepted).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 Unpublished, Accepted. 2024.

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