Initial data identification for the one-dimensional Burgers equation

Liard T, Zuazua Iriondo E (2022)

Publication Language: English

Publication Type: Journal article

Publication year: 2022

Journal

IEEE Transactions on Automatic Control

Book Volume: 67

Pages Range: 3098-3104

Journal Issue: 6

URI: https://ieeexplore.ieee.org/document/9484713

DOI: 10.1109/TAC.2021.3096921

Open Access Link: https://ieeexplore.ieee.org/document/9484713

Abstract

In this paper, we study the problem of identification for 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 property of non-backward uniqueness of Burgers equation, there may exist multiple initial data leading to the same given target. In [13], [17], the authors fully characterize the set of initial data leading to a given target using the classical Lax-Hopf formula. In this note, an alternative proof based only on generalized backward characteristics is given. This leads to the hope of investigate systems of conservation laws in one dimension where the classical Lax-Hopf formula doesn’t hold anymore. Moreover, numerical illustrations are presented using as a target, a function optimized for minimum pressure rise in the context of sonic-boom minimization problems. All of initial data leading to this given target are constructed 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)

Additional Organisation(s)

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

Involved external institutions

National Center for Scientific Research / Centre national de la recherche scientifique (CNRS) FR France (FR)

How to cite

APA:

Liard, T., & Zuazua Iriondo, E. (2022). Initial data identification for the one-dimensional Burgers equation. IEEE Transactions on Automatic Control, 67(6), 3098-3104. https://doi.org/10.1109/TAC.2021.3096921

MLA:

Liard, Thibault, and Enrique Zuazua Iriondo. "Initial data identification for the one-dimensional Burgers equation." IEEE Transactions on Automatic Control 67.6 (2022): 3098-3104.

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