Inverse random source problems for time-harmonic acoustic and elastic waves

Uniqueness and Lipschitz Stability of an Inverse Boundary Value Problem for Time-harmonic Elastic Waves

where Ω is an open and bounded domain with smooth boundary, ∇̂u denotes the strain tensor, ∇̂u := 12 (∇u + (∇u)T ), ψ ∈ H(∂Ω) is the boundary displacement or source, and C ∈ L(Ω) denotes the isotropic elasticity tensor with Lamé parameters λ, μ: C = λI3 ⊗ I3 + 2μIsym, a.e. in Ω, where I3 is 3 × 3 identity matrix and Isym is the fourth order tensor such that IsymA = Â, ρ ∈ L(Ω) is the density, and...

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...

Inverse obstacle scattering for elastic waves

Analysis of the Hessian for inverse scattering problems: II. Inverse medium scattering of acoustic waves

We address the inverse problem for scattering of acoustic waves due to an inhomogeneous medium. We derive and analyze the Hessian in both Hölder and Sobolev spaces. Using an integral equation approach based on Newton potential theory and compact embeddings in Hölder and Sobolev spaces, we show that the Hessian can be decomposed into two components, both of which are shown to be compact operator...

Analysis of the Hessian for inverse scattering problems: I. Inverse shape scattering of acoustic waves

We derive expressions for the shape Hessian operator of the data misfit functional corresponding to the inverse problem of inferring the shape of a scatterer from reflected acoustic waves, using a Banach space setting and the Lagrangian approach. The shape Hessian is then analyzed in both Hölder and Sobolev spaces. Using an integral equation approach and compact embeddings in Hölder and Sobolev...