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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Boundary Stabilization of Parabolic Equations (Hardcover, 1st ed. 2019)
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Boundary Stabilization of Parabolic Equations (Hardcover, 1st ed. 2019)
Series: PNLDE Subseries in Control, 93
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This monograph presents a technique, developed by the author, to
design asymptotically exponentially stabilizing finite-dimensional
boundary proportional-type feedback controllers for nonlinear
parabolic-type equations. The potential control applications of
this technique are wide ranging in many research areas, such as
Newtonian fluid flows modeled by the Navier-Stokes equations;
electrically conducted fluid flows; phase separation modeled by the
Cahn-Hilliard equations; and deterministic or stochastic
semi-linear heat equations arising in biology, chemistry, and
population dynamics modeling. The text provides answers to the
following problems, which are of great practical importance:
Designing the feedback law using a minimal set of eigenfunctions of
the linear operator obtained from the linearized equation around
the target state Designing observers for the considered control
systems Constructing time-discrete controllers requiring only
partial knowledge of the state After reviewing standard notations
and results in functional analysis, linear algebra, probability
theory and PDEs, the author describes his novel stabilization
algorithm. He then demonstrates how this abstract model can be
applied to stabilization problems involving magnetohydrodynamic
equations, stochastic PDEs, nonsteady-states, and more. Boundary
Stabilization of Parabolic Equations will be of particular interest
to researchers in control theory and engineers whose work involves
systems control. Familiarity with linear algebra, operator theory,
functional analysis, partial differential equations, and stochastic
partial differential equations is required.
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