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

Alexander Y. Khapalov is a professor in the Department of Mathematics at Washington State University. 

1. Introduction.- Part I: 2. Continuous observability of the heat equation under a single mobile point sensor.- 3. Continuous observability of the 2-nd order paragolic equations under degenerate mobile sensors.- Part II: 4. Behavior of solutions of the semilinear heat equation in vanishing time and controllability.- 5. Controllability of the semiliniear heat equation with sublinear term and degenerate actuator.- 6. Controllability of the semilinear reaction-diffusion equation with degenerate actuator.- 7. Semilinear parabolic equations: Mobile point controls vs the locally distributed ones.- Part III: 8. Degenerate sensors in source localization and sensor placement problems.- Part IV: 9. Continuous observability of hyperbolic equations under degenerate sensors.- 10. Controllability of the wave equation governed by mobile point controls.- Part V: 11. Exponential decay for the wave equation equipped with a point damping device.- 12. A vibrating string with shuttle-like point dampers and related observability properties.- References.