## Khapalov, Alexander Y.

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

**Table of contents**

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

- Author(s)
- Khapalov, Alexander Y.
- Publisher
- Springer
- Publication year
- 2017
- Language
- en
- Edition
- 1
- Page amount
- 16 pages
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (PDF)
- 9783319604145
- Printed ISBN
- 978-3-319-60413-8