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
Book Volume: 67
Pages Range: 3098-3104
Journal Issue: 6
URI: https://ieeexplore.ieee.org/document/9484713
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)
Involved external institutions
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://dx.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.
BibTeX: Download