ANALYSIS AND NUMERICAL SOLVABILITY OF BACKWARD-FORWARD CONSERVATION LAWS

Liard T, Zuazua Iriondo E (2023)

Publication Type: Journal article

Publication year: 2023

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 55

Pages Range: 1949-1968

Journal Issue: 3

DOI: 10.1137/22M1478720

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 L2(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.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

XLIM : Institut de recherche FR France (FR)

How to cite

APA:

Liard, T., & Zuazua Iriondo, E. (2023). ANALYSIS AND NUMERICAL SOLVABILITY OF BACKWARD-FORWARD CONSERVATION LAWS. SIAM Journal on Mathematical Analysis, 55(3), 1949-1968. https://doi.org/10.1137/22M1478720

MLA:

Liard, Thibault, and Enrique Zuazua Iriondo. "ANALYSIS AND NUMERICAL SOLVABILITY OF BACKWARD-FORWARD CONSERVATION LAWS." SIAM Journal on Mathematical Analysis 55.3 (2023): 1949-1968.

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