Inverse design for the one-dimensional Burgers equation
Liard T, Zuazua E (2019)
Publication Language: English
Publication Type: Other publication type
Publication year: 2019
Abstract
In this paper, we study the problem of inverse design 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 time-irreversibility of the Burgers equation, some target functions are unattainable from solutions of this equation, making the inverse problem under consideration ill-posed. To get around this issue, we introduce an optimal control 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 $L^2(R)$ norm. The two main contributions of this work are the following:
- We fully characterize the set of minimizers of the aforementioned optimal control problem
- A wave-front tracking method is implemented to construct numerically all of them
One of minimizers is the backward entropy solution, constructed using a backward-forward method.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Spain (ES)How to cite
APA:
Liard, T., & Zuazua, E. (2019). Inverse design for the one-dimensional Burgers equation.
MLA:
Liard, Thibault, and Enrique Zuazua. Inverse design for the one-dimensional Burgers equation. 2019.
BibTeX: Download