Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls

DOI10.1051/cocv:1999104zbMath0926.93007OpenAlexW2029901757MaRDI QIDQ4242061

Alexander Y. Khapalov

Publication date: 15 June 1999

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/90561

zbMATH Keywords

approximate controllabilitymultiple solutionssemilinear reaction-diffusion equationinternal lumped control

Mathematics Subject Classification ID

Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Nonlinear parabolic equations (35K55) Nonlinear systems in control theory (93C10)

Related Items

Existence, uniqueness, and stabilization results for parabolic variational inequalities ⋮ A class of globally controllable semilinear heat equations with superlinear terms ⋮ Global non-negative controllability of the semilinear parabolic equation governed by bilinear control ⋮ Stabilization of nonautonomous parabolic equations by a single moving actuator

Cites Work

• Global solutions of reaction-diffusion systems
• Unique continuation for some evolution equations
• A note on approximate controllability for semilinear one-dimensional heat equation
• Finite dimensional null controllability for the semilinear heat equation
• Some aspects of the asymptotic behaviour of the solutions of the semilinear heat equation in vanishing time and approximate controllability
• Observation and prediction for the heat equation
• Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems
• Controllability for Partial Differential Equations of Parabolic Type
• Approximate controllability of the semilinear heat equation
• Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations
• Entire Functions and Muntz-Szasz Type Approximation
• Observability for the one-dimensional heat equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls