On the Dirichlet boundary controllability of the one-dimensional heat equation: semi-analytical calculations and ill-posedness degree

DOI10.1088/0266-5611/27/5/055012zbMath1217.35208OpenAlexW2073755546MaRDI QIDQ3005381

Sidi Mahmoud Kaber, Faker Ben Belgacem

Publication date: 7 June 2011

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/27/5/055012

zbMATH Keywords

heat equation ill-posedness Cauchy matrices Dirichlet boundary controllability

Mathematics Subject Classification ID

Controllability (93B05) Inverse problems for PDEs (35R30) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Eigenvalues, singular values, and eigenvectors (15A18) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

Related Items (13)

A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition ⋮ On the controllability of an advection-diffusion equation with respect to the diffusion parameter: asymptotic analysis and numerical simulations ⋮ Strong convergent approximations of null controls for the 1D heat equation ⋮ Numerical approximation of bang-bang controls for the heat equation: an optimal design approach ⋮ Numerical exact controllability of the 1D heat equation: duality and Carleman weights ⋮ Some inverse and control problems for fluids ⋮ Karhunen-Loève's truncation error for bivariate functions ⋮ On the numerical controllability of the two-dimensional heat, Stokes and Navier-Stokes equations ⋮ A least-squares formulation for the approximation of controls for the Stokes system ⋮ A mixed formulation for the direct approximation of \(L^2\)-weighted controls for the linear heat equation ⋮ Numerical null controllability of the heat equation through a least squares and variational approach ⋮ Null controllability of the heat equation using flatness ⋮ Data Recovery from Cauchy Measurements in Transient Heat Transfer

Uses Software

Matlab

This page was built for publication: On the Dirichlet boundary controllability of the one-dimensional heat equation: semi-analytical calculations and ill-posedness degree