By Triggiani R., Imanuvilov O., Leugering G.
In those fabrics from the convention of May-June 2003, members of those 23 papers describe their paintings on the theoretical and alertness degrees during this self-discipline that has lately elevated significantly by way of extra lifelike versions. normal themes contain elasticity, thermo-elasticity, aero-elasticity, interactions among fluids and elastic constructions, and fluid dynamics, parabolic platforms, dynamical Lame structures, linear and non-linear hyperbolic equations, and pseudo-differential operators on a manifold
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1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Part II: Boundary Control [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
E. 29e) as it will be specified on a case-by-case basis. Steady-state solutions and space V: same as in Eq. 2), Eq. ) given by Eq. 29e) in the strong pointwise form u·ν ≡ 0 on ∂ , and, moreover, in feedback form u = u(y − ye ) via some linear operator y → u, such that, once u(y) is substituted in the translated problem in Eq. 29c), the resulting well-posed, closed-loop system in Eqs. 29a–d) possesses the following desirable property: the steady-state solutions ye defined in Eq. 2) are locally exponentially stable.
3 Part II: Boundary Control [3] 37 This yields a “combined index” of unboundedness strictly greater than 32 . By contrast, the established (and rich) optimal control theory of boundary control parabolic problems and corresponding algebraic Riccati theory requires a “combined index” of unboundedness strictly less than 1 (see Reference 12, Vol. 1, in particular, pp. 501–503), which is the maximum limit handled by perturbation theory of analytic semigroups. To implement this program, however, one must first overcome, at the very outset, the preliminary stumbling obstacle of showing that the present highly nonstandard OCP—with the aforementioned high level of combined unboundedness in control and observation operators and further restricted within the class of tangential boundary controllers—is, in fact, nonempty.