Existence of Insensitizing Controls for a Semilinear Heat Equation with a Superlinear Nonlinearity

DOI10.1081/PDE-200033749zbMath1067.93035MaRDI QIDQ3157921

Olivier Bodart, Rosario Pérez-García, Manuel González-Burgos

Publication date: 20 January 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

controllabilityheat equationDirichlet boundary conditionsCarleman estimatessemilinear equationnonlinear partial differential equationinsensitizing controlfixed-point techniqueregularizing properties

Mathematics Subject Classification ID

Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Nonlinear parabolic equations (35K55)

Related Items (27)

Global sensitivity analysis for the boundary control of an open channel ⋮ Remarks on the Control of Two-Phase Stefan Free-Boundary Problems ⋮ Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient ⋮ Insensitizing controls for a phase field system ⋮ Insensitizing controls for the parabolic equations with dynamic boundary conditions ⋮ Positive and negative results on the internal controllability of parabolic equations coupled by zero- and first-order terms ⋮ Some control problems for the Burgers equation ⋮ Remarks on the controllability of parabolic systems with non-diagonalizable diffusion matrix ⋮ Locally distributed desensitizing controls for the wave equation ⋮ Nash equilibria strategies and equivalent single-objective optimization problems: the case of linear partial differential equations ⋮ Insensitizing control problem for the Hirota-Satsuma system of KdV-KdV type ⋮ Observability Inequalities on Measurable Sets for the Stokes System and Applications ⋮ Insensitizing controls for a forward stochastic heat equation ⋮ Controllability of cascade coupled systems of multi-dimensional evolution PDEs by a reduced number of controls ⋮ Insensitizing controls for the Navier-Stokes equations ⋮ Insensitizing exact controls for the scalar wave equation and exact controllability of 2-coupled cascade systems of PDE's by a single control ⋮ Controllability of systems of Stokes equations with one control force: existence of insensitizing controls ⋮ Exact controllability to trajectories for a semilinear heat equation with a superlinear nonlinearity ⋮ Controllability results for cascade systems of \(m\) coupled parabolic PDEs by one control force ⋮ Insensitizing controls for a class of nonlinear Ginzburg-Landau equations ⋮ An insensitizing control problem for the Ginzburg-Landau equation ⋮ -Insensitizing controls for the linear stochastic Korteweg-de Vries equation ⋮ Null-Controllability of Two Species Reaction-Diffusion System with Nonlinear Coupling: A New Duality Method ⋮ Insensitizing controls for a semilinear parabolic equation: a numerical approach ⋮ Insensitizing controls of a 1D Stefan problem for the semilinear heat equation ⋮ Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity ⋮ Null controllability with constraints on the state for the 1-D Kuramoto-Sivashinsky equation

Cites Work

• Unnamed Item
• Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
• Exact controllability of the superlinear heat equation
• Null and approximate controllability for weakly blowing up semilinear heat equations
• Controls insensitizing the norm of the solution of a semilinear heat equation
• Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
• On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient
• Null controllability of nonlinear convective heat equations
• Insensitizing controls for a semilinear heat equation

This page was built for publication: Existence of Insensitizing Controls for a Semilinear Heat Equation with a Superlinear Nonlinearity