Controllability of partial differential equations governed by multiplicative controls

✍ Scribed by Alexander Y. Khapalov (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2010
• Tongue: English
• Leaves: 305
• Series: Lecture Notes in Mathematics 1995
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
Introduction....Pages 1-12
Front Matter....Pages 14-14
Global Nonnegative Controllability of the 1- D Semilinear Parabolic Equation....Pages 15-31
Multiplicative Controllability of the Semilinear Parabolic Equation: A Qualitative Approach....Pages 33-48
The Case of the Reaction-Diffusion Term Satisfying Newton’s Law....Pages 49-65
Classical Controllability for the Semilinear Parabolic Equations with Superlinear Terms....Pages 67-80
Front Matter....Pages 82-82
Controllability Properties of a Vibrating String with Variable Axial Load and Damping Gain....Pages 83-104
Controllability Properties of a Vibrating String with Variable Axial Load Only....Pages 105-119
Reachability of Nonnegative Equilibrium States for the Semilinear Vibrating String....Pages 121-145
The 1- D Wave and Rod Equations Governed by Controls That Are Time-Dependent Only....Pages 147-156
Front Matter....Pages 158-158
Introduction....Pages 159-164
A “Basic” 2- D Swimming Model....Pages 165-170
The Well-Posedness of a 2-D Swimming Model....Pages 171-193
Geometric Aspects of Controllability for a Swimming Phenomenon....Pages 195-217
Local Controllability for a Swimming Model....Pages 219-236
Global Controllability for a “Rowing” Swimming Model....Pages 237-262
Front Matter....Pages 264-264
Multiplicative Controllability for the Schrödinger Equation....Pages 265-274
Back Matter....Pages 275-290

✦ Subjects

Partial Differential Equations; Systems Theory, Control; Calculus of Variations and Optimal Control, Optimization; Mathematical Biology in General; Engineering Fluid Dynamics