Mobile Point Sensors and Actuators in the Controllability Theory of Partial Differential Equations

1. Introduction
Alexander Y. Khapalov

Part I. Observability and Controllability of Linear Parabolic Equations by Means of Degenerate Sensors and Controls

2. Continuous Observability of the Heat Equation Under a Single Mobile Point Sensor
Alexander Y. Khapalov

3. Continuous Observability of Second-Order Parabolic Equations Under Degenerate Mobile Sensors
Alexander Y. Khapalov

Part II. Observability and Controllability of Semilinear Parabolic Equations by Means of Degenerate Sensors and Controls

4. Behavior of Solutions of the Semilinear Heat Equation in Vanishing Time and Controllability
Alexander Y. Khapalov

5. Controllability of the Semilinear Heat Equation with a Sublinear Term and a Degenerate Actuator
Alexander Y. Khapalov

6. Controllability of the Semilinear Reaction–Diffusion Equation with a Degenerate Actuator
Alexander Y. Khapalov

7. Semilinear Parabolic Equations: Mobile Point Controls Versus Locally Distributed Ones
Alexander Y. Khapalov

Part III. Source Localization and Sensor Placement in Environmental Monitoring

8. Degenerate Sensors in Source Localization and Sensor Placement Problems
Alexander Y. Khapalov

Part IV. Observability and Controllability of Hyperbolic Equations by Means of Degenerate Sensors and Actuators

9. Continuous Observability of Hyperbolic Equations under Degenerate Sensors
Alexander Y. Khapalov

10. Controllability of the Wave Equation Governed by Mobile Point Controls
Alexander Y. Khapalov

Part V. Observability and Stabilizability of a Vibrating String by Means of Degenerate Sensors and Damping

11. Exponential Decay for the Wave Equation Equipped with a Point Damping Device
Alexander Y. Khapalov

12. A Vibrating String with Shuttle-Like Point Dampers and Related Observability Properties
Alexander Y. Khapalov

Keywords: Mathematics, Partial Differential Equations, Systems Theory, Control