Webb21 dec. 2007 · A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations Published online by Cambridge University Press: 21 December 2007 Louis Tebou Article Metrics Get access Cite Abstract First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. Webbinteresting feature of his bound is that, for A normal, it reduces to the usual estimate (zI −A)−1 ≤ 1 d(z,σ(A)). His proof relies on an adaptation of finite-dimensional arguments which can be traced to work of Henrici from the early sixties [Hen]. The estimate of Dechevski and Persson, obtained by different methods, does not rely
Carleman estimates and controllability results for fully discrete ...
WebbThe first one concerns the new Carleman estimates that we need to prove for such systems. We aim to solve our different inverse problems using the observation of only one component, the pressure P $$ P $$ , or the temperature θ $$ \theta $$ by adapting the Carleman estimate proved in part I, Theorem 1.1 in [ 5 ]. Webb1 nov. 2024 · The key improvements are: (1) we obtain smaller observation regions when compared with standard Carleman estimate results, and (2) we also address the case when observability is centered around a ... sterling isa contact number
Carleman Estimate for Stochastic Parabolic Equations and Inverse …
WebbWe prove it in several stages. First, we obtain equations for functions Dk t (u 1 − u 2), k= 3,4, because these equations are more convenient to work with. This is done in Section 2. Also, in this section we formulate our key Carleman estimate for a hyperbolic operator (Lemma 2.1) and two more lemmata. Next, we prove three new Carleman estimates. WebbA Carleman estimate is an L2 -weighted estimate for solutions to system (1.1), and is stated as follows: by choosing a weight function ϕ = ϕ (x, t), there exist constants C > 0 and s0 > 0 such that Z Z Z 3 2 2sϕ 2 2sϕ s u e dxdt ≤ C Lu e dxdt + C ∇x,t u 2e2sϕ dΣ (1.3) Ω×I Ω×I ∂ (Ω×I) for all s ≥ s0 . Webb25 nov. 2024 · The general theory of Carleman estimates does not cover many important systems in mathematical physics such as the Lamé equations, and for them we have to … pirate bay torrentz2 download