Controllability of partial differential equationsgoverned by multiplicative controls

The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems. Physically motivated, mathematically challenging and timely Relatively few results are available in the field The results described in this book are certainly novel and original INDICE: 1. Introduction.- Part I Multiplicative Controllability of Parabolic Equations.- 2. Global Nonnegative Controllability of the 1-D Semilinear Parabolic Equation.- 3. Multiplicative Controllability of the Semilinear Parabolic Equation: A Qualitative Approach.- 4. The Case of the Reaction-Diffusion Term Satisfying Newton’s Law.- Part II Multiplicative Controllability of Hyperbolic Equations.- 6. Controllability Properties of a Vibrating String with Variable Axial Load and Damping Gain.- 7. Controllability Properties of a Vibrating String with Variable Axial Load Only.- 8. Reachability of Nonnegative Equilibrium States for the Semilinear Vibrating String.- 9. The 1-D Wave and Rod Equations Governed by Controls That Are Time-Dependent Only.- Part III Controllability for Swimming Phenomenon.- 10. Introduction.- 11. A “Basic” 2-D Swimming Model.- 12. The Well-Posedness of a 2-D Swimming Model.- 13. Geometric Aspects of Controllability for a Swimming Phenomenon.- 14. Local Controllability for a Swimming Model.- 15. Global Controllability for a ”Rowing” Swimming Model.- Part IV Multiplicative Controllability Properties of the Schrödinger Equation.- 16. Multiplicative Controllability for the Schrödinger Equation.

• ISBN: 978-3-642-12412-9
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 282
• Fecha Publicación: 01/05/2010
• Nº Volúmenes: 1
• Idioma: Inglés