Observability and uniqueness theorem for a coupled hyperbolic system

Existence and Uniqueness for a Variational Hyperbolic System without Resonance

Uniqueness Theorem for Abstract Hyperbolic Equations with Application to the Uniqueness of the Harmonic Coordinate System in General Relativity

An analog of the radiation condition is found for an abstract hyperbolic equation. When this condition holds, the uniqueness theorem for a&z&u) &(p8,u) + Au = f is valid. Here n, p, and A are some linear operators depending on t and Y. For example, Eq. 0 u = &(uoo(t, X) 8,~) &(u$~u) + q(t, x) u = f is of such a type. In what follows a, = a/a, , ai = a/axi , a, = a/a,. , x = (XI )...) xN), 1 < i...

Flux Observability for Hyperbolic Systems

The aim of this paper is to introduce the concept of boundary gradient observability for distributed hyperbolic systems evolving in spatial domain Ω , and which the gradient state is to be observed on a boundary subregion Γ of ∂Ω . We give definitions and characterizations and some properties of this kind of regional boundary observability. To explore this notion we describe an new approach to ...

Blowup estimates for observability of a thermoelastic coupled system

Sharp blowup rates are established for the minimal energy (equivalently, for observability estimates) when the control time T → 0. As in, e.g., [10], [14], [12] the blowup estimates obtained with boundary controls are of the order eO(1/T ) and, as specified by the finite dimensional analysis of [11], are of the order O(T−5/2) for the case of internal controls. The dependence of these blowup est...

A Uniqueness Theorem for Clustering

Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like “What distinguishes a clustering of data from other data partitioning?”, “Are there any principles governing all clustering paradigms?”, “How should a user choose an appropriate clustering algorithm for a particular task?”, etc. are almost completely unanswered by the e...