Some stability inequalities for hybrid inverse problems
نویسندگان
چکیده
We study some hybrid inverse problems associated to BVP’s for Schrödinger and Helmholtz type equations. The we consider consist in the determination of coefficients from knowledge internal energy densities. establish local Lipschitz stability inequalities as well Hölder inequalities.
منابع مشابه
global results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Stability of Solutions for Some Inverse Problems
In this article we establish three stability results for some inverse problems. More precisely we consider the following boundary value problem: ∆u + λu + μ = 0 in Ω, u = 0 on ∂Ω, where λ and μ are real constants and Ω ⊂ R2 is a smooth bounded simply-connected open set. The inverse problem consists in the identification of λ and μ from knowledge of the normal flux ∂u/∂ν on ∂Ω corresponding to s...
متن کاملOracle Inequalities for Inverse Problems
We consider a sequence space model of statistical linear inverse problems where we need to estimate a function f from indirect noisy observations. Let a nite set of linear estimators be given. Our aim is to mimic the estimator in that has the smallest risk on the true f. Under general conditions, we show that this can be achieved by simple minimization of unbiased risk estimator, provided the s...
متن کاملHybrid Samplers for Ill-Posed Inverse Problems
In the Bayesian approach to ill-posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distrib...
متن کاملReconstructions for some coupled-physics inverse problems
This letter announces and summarizes results obtained in [8] and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from knowledge of a sufficiently large number of its solutions. We present this derivation and extend it to show which parameters may or may not be reconstructed for several h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2022
ISSN: ['1631-073X', '1778-3569']
DOI: https://doi.org/10.5802/crmath.262