On the cost of null controllability of a fourth-order parabolic equation

DOI10.1016/j.jde.2016.08.042zbMath1361.35071OpenAlexW2515260177MaRDI QIDQ324125

Nicolás Carreño, Patricio Guzmán

Publication date: 10 October 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.08.042

zbMATH Keywords

boundary controlfourth-order parabolic equationCarleman estimatescost of null controllabilityuniform null controllability

Mathematics Subject Classification ID

Controllability (93B05) Initial-boundary value problems for higher-order parabolic equations (35K35) Singular perturbations in context of PDEs (35B25) Observability (93B07)

Related Items

Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates, Carleman estimate and null controllability of a fourth order parabolic equation in dimension \(N\geq 2\), Determination of the space-dependent source term in a fourth-order parabolic problem, Cost of null controllability for parabolic equations with vanishing diffusivity and a transport term, Lipschitz stability of an inverse source problem for ADMB-KdV equation, Recovery of the time‐dependent zero‐order coefficient in a fourth‐order parabolic problem, The cost of null controllability for a backward stochastic degenerate parabolic equation in the vanishing viscosity limit, The null boundary controllability for a fourth-order parabolic equation with Samarskii-Lonkin-type boundary conditions, Controllability of a simplified time-discrete stabilized Kuramoto-Sivashinsky system, An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation, Uniform null controllability of a fourth-order parabolic equation with a transport term, Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation, Local exact controllability to the trajectories of the Cahn-Hilliard equation, Boundary controllability of a cascade system coupling fourth- and second-order parabolic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local controllability of the stabilized Kuramoto-Sivashinsky system by a single control acting on the heat equation
• 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
• Local exact controllability to the trajectories of the 1-D Kuramoto-Sivashinsky equation
• A new global Carleman estimate for Cahn-Hilliard type equation and its applications
• Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation
• A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit
• Infinite-dimensional dynamical systems in mechanics and physics.
• Local exact controllability of the Navier-Stokes system
• Observability estimate and null controllability for one-dimensional fourth order parabolic equation
• A new global Carleman estimate for the one-dimensional Kuramoto-Sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem
• Lipschitz stability in an inverse problem for the main coefficient of a Kuramoto-Sivashinsky type equation
• Exact controllability theorems for linear parabolic equations in one space dimension
• Lipschitz stability in an inverse problem for the Kuramoto–Sivashinsky equation
• On the non-uniform null controllability of a linear KdV equation
• Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit
• UNIFORM CONTROLLABILITY OF A TRANSPORT EQUATION IN ZERO DIFFUSION–DISPERSION LIMIT
• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• Insensitizing controls for the Cahn-Hilliard type equation