Controllability of Partial Differential Equations Governed by Multiplicative Controls
Khapalov, Alexander Y.
Controllability of Partial Differential Equations Governed by Multiplicative Controls [electronic resource] / by Alexander Y. Khapalov. - XV, 284 p. 26 illus. online resource. - Lecture Notes in Mathematics, 1995 0075-8434 ; . - Lecture Notes in Mathematics, 1995 .
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.
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.
9783642124136
10.1007/978-3-642-12413-6 doi
Differential equations, partial.
Systems theory.
Mathematical optimization.
Hydraulic engineering.
Partial Differential Equations.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Mathematical and Computational Biology.
Engineering Fluid Dynamics.
QA370-380
515.353
Controllability of Partial Differential Equations Governed by Multiplicative Controls [electronic resource] / by Alexander Y. Khapalov. - XV, 284 p. 26 illus. online resource. - Lecture Notes in Mathematics, 1995 0075-8434 ; . - Lecture Notes in Mathematics, 1995 .
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.
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.
9783642124136
10.1007/978-3-642-12413-6 doi
Differential equations, partial.
Systems theory.
Mathematical optimization.
Hydraulic engineering.
Partial Differential Equations.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Mathematical and Computational Biology.
Engineering Fluid Dynamics.
QA370-380
515.353