Controllability of Partial Differential Equations Governed by Multiplicative Controls

1. Auflage 2010
ISBN: 978-3-642-12412-9
Verlag: Springer

Buch, Englisch, Band 1995, 284 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 960 g

Reihe: Lecture Notes in Mathematics

In a typical mathematical model of a controlled distributed parameter process one usually ?nds either boundary or internal locally distributed controls to serve as the means to describe the effect of external actuators on the process at hand. H- ever,these classical controls, enteringthe modelequationsas additive terms, are not suitable to deal with a vast array of processes that can change their principal intr- sic properties due to the control actions. Important examples here include (but not limitedto)thechainreaction-typeprocessesinbiomedical,nuclear,chemicalan- nancial applications, which can changetheir (reaction)rate when certain “catalysts” are applied, and the so-called “smart materials”, which can, for instance, alter their frequency response. The goal of this monograph is to address the issue of global controllability of partial differential equations in the context of multiplicative (or bilinear) c- trols, which enter the model equations as coef?cients. The mathematical models of our interest include the linear and nonlinear parabolic and hyperbolic PDE’s, the Schrodi ¨ nger equation, and coupled hybrid nonlinear distributed parameter systems associated with the swimming phenomenon. Pullman, WA, USA Alexander Khapalov January 2010 vii Preface This monograph developed from the research conducted in 2001–2009 in the area of controllability theory of partial differential equations. The concept of control- bility is a principal component of Control Theory which was brought to life in the 1950’s by numerous applications in engineering, and has received the most sign- icant attention both from the engineering and the mathematical communities since then.

Zielgruppe

Research

Autoren/Hrsg.

Khapalov, Alexander Y.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Multiplicative Controllability of Parabolic Equations.- Global Nonnegative Controllability of the 1-D Semilinear Parabolic Equation.- Multiplicative Controllability of the Semilinear Parabolic Equation: A Qualitative Approach.- The Case of the Reaction-Diffusion Term Satisfying Newton’s Law.- Classical Controllability for the Semilinear Parabolic Equations with Superlinear Terms.- Multiplicative Controllability of Hyperbolic Equations.- Controllability Properties of a Vibrating String with Variable Axial Load and Damping Gain.- Controllability Properties of a Vibrating String with Variable Axial Load Only.- Reachability of Nonnegative Equilibrium States for the Semilinear Vibrating String.- The 1-D Wave and Rod Equations Governed by Controls That Are Time-Dependent Only.- Controllability for Swimming Phenomenon.- A “Basic” 2-D Swimming Model.- The Well-Posedness of a 2-D Swimming Model.- Geometric Aspects of Controllability for a Swimming Phenomenon.- Local Controllability for a Swimming Model.- Global Controllability for a “Rowing” Swimming Model.- Multiplicative Controllability Properties of the Schrodinger Equation.- Multiplicative Controllability for the Schrödinger Equation.