The proof of key carleman estimate
WebbThe proofs are based on a Carleman estimate where the weight function depends on H. 1. Introduction and main results Let Ω ⊂ Rn be a bounded domain with smooth boundary and H = (h1 , ..., hn ) ∈ (C 1 (Ω))n . Let (x·y) and x denote the scalar product of x, y ∈ Rn and the norm of x ∈ Rn , respectively. Webbin the classical proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution with the exponential rate. …
The proof of key carleman estimate
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Webb10 sep. 2024 · In this paper, we prove a Carleman estimate for fully discrete approximations of one-dimensional parabolic operators in which the discrete parameters h and t are connected to the large Carleman parameter. We use this estimate to obtain relaxed observability inequalities which yield, by duality, controllability results for fully … Webbin determining u,v in Ω × (ε,T) only by u(·,0),v(·,0) in Ω. Moreover our key Carleman estimate readily produces the global Lipschitz stability if we can use u ... We prove a key estimate of Carleman type with two large parameters. We set ϕ(t) = eλt, where a constant λ > 0 is chosen later. Theorem 2.1.
Webb1 juni 2024 · In this paper, we prove the stability and convergence of a coefficient inverse problem for the semi-discrete Schrödinger equation by means of an appropriate … Webb31 okt. 2024 · This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations,...
Webb20 maj 2024 · A Carleman estimate for a certain rst order elliptic system is proved. The proof is elementary and does not rely on pseudo-di erential calculus. This estimate is … 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
WebbCarleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations Loc H. Nguyen∗ Michael V. Klibanov† Abstract The main …
WebbCarleman estimate and proves conditional stability for both problems. Key words. Fourh-order parabolic equation, inverse source problem, continuation, Carle-man estimate, … dfw chevyWebbIn this paper, the authors consider inverse problems of determining a coefficient or a source term in an ultrahyperbolic equation by some lateral boundary data. The authors prove Hölder estimates which are global and local and the key tool is Carlema ... chv40145 castleWebb31 maj 2024 · domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carleman estimate to a lateral Cauchy problem for the … chv2o1 charter of rights and freedomsWebb19 sep. 2012 · Proof. We divide the proof into five steps. The key is Carleman estimates. Step 1. Our argument is a modification of, e.g., [4, 18] and is based on the Carleman … chv3/cambsedWebb916 I. Naki´c, C. Rose and M. Tautenhahn the references therein. Further applications of Carleman estimates are, for example, uniqueness properties of solutions of Schr¨odinger chv40147 calgary trailWebbA 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 . dfw chevy car dealershipsWebbFor the isotropic stationary Lamé system with variable coefficients equipped with the Dirichlet or surface stress boundary condition, we obtain a Carleman estimate such that (i) the right hand side is estimated in a weighted L 2-space and (ii) the estimate includes nonhomogeneous surface displacement or surface stress. Using this estimate we … dfw child care services