Skip to content
  • Publications
  • Jobs
  • enzuazua
  • Seminars
  • Events Calendar
cmc.deusto.eus
  • Home
  • About us
    • About the Chair
    • Head of the Chair
    • Team
    • Past Members
  • Research
    • Projects
    • ERC CoDeFeL
    • Research Group in Computational Mathematics
    • 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 by year
      • Publications 2025
      • Publications 2024
      • Publications 2023
      • 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

Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term

Bárcena-Petisco J.A., Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term (2020). HAL Id: hal-02455632

Abstract. In this paper we consider the heat equation with Neumann, Robin and mixed boundary conditions (with coefficients on the boundary which depend on the space variable). The main results concern the behaviour of the cost of the null controllability with respect to the diffusivity when the control acts in the interior. First, we prove that if we almost have Dirichlet boundary conditions in the part of the boundary in which the flux of the transport enters, the cost of the controllability decays for a time T sufficiently large. Next, we show some examples of Neumann and mixed boundary conditions in which for any time T > 0 the cost explodes exponentially as the diffusivity vanishes. Finally, we study the cost of the problem with Neumann boundary conditions when the control is localized in the whole domain.

Read Full Paper

Tags:
heat equationsingular limitsspectral decompositiontransport equationuniform controllability

Post navigation

Previous Post
CONVADP CONVADP
Next Post
Control of reaction-diffusion under state constraints – Heterogeneous setting: Gene-flow Control of reaction-diffusion under state constraints – Heterogeneous setting: Gene-flow

Last Publications

Regional and Partial Observability and Control of Waves

Cluster-based classification with neural ODEs via control

Optimal convergence rates for the finite element approximation of the Sobolev constant

Boundary observation and control for fractional heat and wave equations

Almost periodic turnpike phenomenon for time-dependent systems

  • DeustoCCM seminar: Controllability on some PDEs with dynamic boundary conditions
  • Regional and Partial Observability and Control of Waves
  • Cluster-based classification with neural ODEs via control
  • Optimal convergence rates for the finite element approximation of the Sobolev constant
  • Boundary observation and control for fractional heat and wave equations
Copyright 2016 - 2025 — cmc.deusto.eus. 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