TY  - BOOK
AU  - Khapalov,Alexander Y.
ED  - SpringerLink (Online service)
TI  - Controllability of Partial Differential Equations Governed by Multiplicative Controls
T2  - Lecture Notes in Mathematics,
SN  - 9783642124136
AV  - QA370-380 
U1  - 515.353 23
PY  - 2010///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Differential equations, partial
KW  - Biology
KW  - Systems theory
KW  - Hydraulic engineering
KW  - Partial Differential Equations
KW  - Systems Theory, Control
KW  - Calculus of Variations and Optimal Control, Optimization
KW  - Mathematical Biology in General
KW  - Engineering Fluid Dynamics
N1  - 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
N2  - 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
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-3-642-12413-6
ER  -