Download Control Theory for Partial Differential Equations: Volume 2, by Irena Lasiecka, Roberto Triggiani PDF

By Irena Lasiecka, Roberto Triggiani

Volume II makes a speciality of the optimum regulate challenge over a finite time period for hyperbolic dynamical platforms. The chapters examine a few summary versions, every one prompted through a specific canonical hyperbolic dynamics, and current quite a few new effects.

Show description

Read Online or Download Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon: Continuous and Approximation Theories (Encyclopedia of Mathematics and Its Applications Series, Book 75) PDF

Similar differential equations books

Elementary Differential Equations and Boundary Value Problems (7th Edition)

This ebook covers the entire crucial issues on differential equations, together with sequence recommendations, Laplace transforms, platforms of equations, numerical equipment and part airplane tools. transparent causes are precise with many present examples.

Numerical solution of partial differential equations

This moment variation of a hugely profitable graduate textual content provides an entire creation to partial differential equations and numerical research. Revised to incorporate new sections on finite quantity tools, converted equation research, and multigrid and conjugate gradient tools, the second one version brings the reader up to date with the most recent theoretical and business advancements.

Multigrid Methods

Multigrid provides either an ordinary advent to multigrid tools for fixing partial differential equations and a modern survey of complicated multigrid strategies and real-life functions. Multigrid equipment are priceless to researchers in medical disciplines together with physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines.

Methods of Nonlinear Analysis: Applications to Differential Equations (Birkhauser Advanced Texts Basler Lehrbucher)

During this booklet, the elemental equipment of nonlinear research are emphasised and illustrated in easy examples. each thought of strategy is prompted, defined in a basic shape yet within the easiest attainable summary framework. Its purposes are proven, quite to boundary worth difficulties for straightforward traditional or partial differential equations.

Additional info for Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon: Continuous and Approximation Theories (Encyclopedia of Mathematics and Its Applications Series, Book 75)

Example text

Although the study of this fully pathological case is deferred to the technical treatment of Chapter 16 (in Volume 3), in the present Chapter 8 we consider two different subsettings on two parallel tracks. 2), respectively. Our primary emphasis is on the first case where an observation operator R is present, bounded from a state space Y to an output space Z, such that the composition R Lo is better behaved than each of its components viewed separately. 1, the operator RLo is, in fact, continuous between the input space L2(0, T; U) and the output space C([O, T]; Z).

V); (Bu, y)y = (u, B*y)u. 1) with feedback control u = -EB*x, where E > 0: x + Ax + EBB*i = 0; A. 8) V(B*) : [A! Yl - EA-! )}. 2 Main Regularity Results The usual dissipativity arguments leading to the Lumer-Phillips theorem [Pazy, 1983, p. 14] or its corollary [Pazy, 1983, p. 15] yield a generation result. 2). c. contraction semigroups eA,t and e A:t on Y, t ~ O. Proof. We limit ourselves to dissipativity. 2) V Ai . 4). 4) where, moreover, we now assume the following hypothesis. 3). With E > 0 fixed, eA,t is exponentially stable on Y: There exist constants M ~ 1 and 8 > 0 (depending on E), such that Il eA,tll £(Y) = Ile(A-fBB*)tll £(Y) -< Me- 8t , t ~ O.

2. 1.

Download PDF sample

Rated 4.15 of 5 – based on 8 votes