Skip to content
  • Publications
  • Jobs
  • enzuazua
  • Seminars
  • Events Calendar
  • Home
  • About us
    • About the Chair
    • Head of the Chair
    • Team
    • Past Members
  • Research
    • Projects
    • ERC – DyCon
    • DyCon Blog
    • DyCon Toolbox
    • Industrial & Social TransferenceContents related to the industrial and social transference aspects of the work in the Chair of Computational Mathematics.
  • Publications
    • Publications (All)
    • Publications Relased
      • Publications 2022
      • Publications 2021
      • Publications 2020
      • Publications 2019
      • Publications 2018
      • Publications 2017
      • Publications 2016
    • AcceptedAccepted to be released
    • SubmittedSubmitted publications
  • Activities
    • Events calendar
    • Past Events
    • News
    • Seminars
    • Courses
    • enzuazua
    • Gallery
  • Jobs
  • Contact

Inverse design for the one-dimensional Burgers equation

T. Liard, E. Zuazua. Inverse design for the one-dimensional Burgers equation. (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.

Read Full Paper

Last updated on March 17, 2022

Post navigation

Previous Post
Quantitative touchdown localization for the MEMS problem with variable dielectric permittivity
Next Post
Upper bounds for the decay rate in a nonlocal p-Laplacian evolution problem

Last Publications

Optimal actuator design via Brunovsky’s normal form

Stability and Convergence of a Randomized Model Predictive Control Strategy

Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems

Control of certain parabolic models from biology and social sciences

Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation

  • Postdoc at DASEL project -Open position
  • FAU MoD Lecture: Applications of AAA Rational Approximation
  • DASEL
  • Optimal actuator design via Brunovsky’s normal form
  • ERC DyCon Impact Dimension (2016-2022)
  • Postdoc at DASEL project -Open position
  • FAU MoD Lecture: Applications of AAA Rational Approximation
  • DASEL
  • Optimal actuator design via Brunovsky’s normal form
  • ERC DyCon Impact Dimension (2016-2022)
Copyright 2016 - 2023 — . All rights reserved. Chair of Computational Mathematics, Deusto Foundation - University of Deusto
Scroll to Top
  • Aviso Legal
  • Política de Privacidad
  • Política de Cookies
  • Configuración de Cookies
WE USE COOKIES ON THIS SITE TO ENHANCE USER EXPERIENCE. We also use analytics. By navigating any page you are giving your consent for us to set cookies.    more information
Privacidad