Liard T, Zuazua E (2019)

**Publication Language:** English

**Publication Type:** Other publication type

**Publication year:** 2019

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.

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

**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