On the Reachable Set for the One-Dimensional Heat Equation
From MaRDI portal
Publication:4641756
DOI10.1137/16M1093215zbMath1391.35171arXiv1609.02692OpenAlexW2963936862MaRDI QIDQ4641756
Jérémi Dardé, Sylvain Ervedoza
Publication date: 18 May 2018
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1609.02692
Heat equation (35K05) Attainable sets, reachability (93B03) Integral equations with kernels of Cauchy type (45E05)
Related Items
Reachable Space of the Hermite Heat Equation with Boundary Control ⋮ Controllability problems for the heat equation on a half-axis with a bounded control in the Neumann boundary condition ⋮ Reachable states for the distributed control of the heat equation ⋮ Analytic properties of heat equation solutions and reachable sets ⋮ Reachability results for perturbed heat equations ⋮ Small-time global exact controllability of the Navier-Stokes equation with Navier slip-with-friction boundary conditions ⋮ Controllability problems for the heat equation with variable coefficients on a half-axis ⋮ Precise estimates for biorthogonal families under asymptotic gap conditions ⋮ Minimal time issues for the observability of Grushin-type equations ⋮ Sharp reachability results for the heat equation in one space dimension ⋮ On the cost of observability in small times for the one-dimensional heat equation ⋮ Exact controllability of semilinear heat equations in spaces of analytic functions ⋮ On the controllability of an advection-diffusion equation with respect to the diffusion parameter: asymptotic analysis and numerical simulations ⋮ Observability and control of parabolic equations on networks with loops ⋮ Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition ⋮ Reachable states for infinite-dimensional linear systems: old and new ⋮ From the reachable space of the heat equation to Hilbert spaces of holomorphic functions ⋮ Reachable states and holomorphic function spaces for the 1-D heat equation ⋮ Separation of singularities for the Bergman space and application to control theory ⋮ The reachable space of the heat equation for a finite rod as a reproducing kernel Hilbert space ⋮ Exact Controllability of a Linear Korteweg--de Vries Equation by the Flatness Approach
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation
- Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport-diffusion equation
- Hardy uncertainty principle, convexity and parabolic evolutions
- The cost of controlling weakly degenerate parabolic equations by boundary controls
- Sharp observability estimates for heat equations
- Time-invariance of the reachable set for linear control problems
- Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time
- From the reachable space of the heat equation to Hilbert spaces of holomorphic functions
- Null controllability of the heat equation using flatness
- Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach
- An application of a conjecture due to Ervedoza and Zuazua concerning the observability of the heat equation in small time to a conjecture due to Coron and Guerrero concerning the uniform controllability of a convection-diffusion equation in the vanishing viscosity limit
- On exponential observability estimates for the heat semigroup with explicit rates
- New blow-up rates for fast controls of Schrödinger and heat equations
- Exact controllability theorems for linear parabolic equations in one space dimension
- The Calderón problem with partial data
- Some trigonometrical inequalities with applications to the theory of series
- Null Controllability of One-dimensional Parabolic Equations by the Flatness Approach
- A Deterministic Optimal Design Problem for the Heat Equation
- The Control Transmutation Method and the Cost of Fast Controls
- The bergman space on a sector and the heat equation
- Exact Controllability, Stabilization and Perturbations for Distributed Systems
- A General Theory of Observation and Control
- Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
- Contróle Exact De Léquation De La Chaleur
- On the Reachable States for the Boundary Control of the Heat Equation