اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDirect and inverse scattering problem by an unbounded rough interface with buried obstacles
53
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we consider the direct and inverse problem of scattering of time-harmonic waves by an unbounded rough interface with a buried impenetrable obstacle. We first study the well-posedness of the direct problem with a local source by the variational method; the well-posedness result is then extended to scattering problems induced by point source waves (PSWs) and hyper-singular point source waves (HSPSWs). For PSW or HSPSW incident waves, the induced total field admits a uniformly bounded estimate in any compact subset far from the source position. Moreover, we show that the scattered field due to HSPSWs can be approximated by the scattered fields due to PSWs. With these properties and a novel reciprocity relation of the total field, we prove that the rough surface and the buried obstacle can be uniquely determined by the scattered near-field data measured only on a line segment above the rough surface. The proof substantially relies upon constructing a well-posed interior transmission problem for the Helmholtz equation.
قيم البحث
اقرأ أيضاً
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave measurements on a bo
unded line segment above the surface, based on reconstructing a modified near-field equation associated with a special surface, which generalized our pervious work for the Helmholtz equation (SIAM J. IMAGING. SCI. 10(3)(2017), 1579-1602) to the Navier equation. Several numerical examples are carried out to illustrate the effectiveness of the inversion algorithm.
We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flux at the boundary. The attenuation and scattering coefficients are kno
wn and the unknown source is isotropic. The approach is based on the Cauchy problem for a Beltrami-like equation for the sequence valued maps, and extends the original ideas of A. Bukhgeim from the non-scattering to scattering media. We demonstrate the feasibility of the method in a numerical experiment in which the scattering is modeled by the two dimensional Henyey-Greenstein kernel with parameters meaningful in Optical Tomography.
A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the boundary of
the domain, apart from imposing that the boundary of the domain is $C^{1,1}$. The coefficients are assumed to coincide on a neighbourhood of the boundary, a natural property in applications.
We prove the Kato conjecture for elliptic operators, $L=- ablacdotleft((mathbf A+mathbf D) abla right)$, with $mathbf A$ a complex measurable bounded coercive matrix and $mathbf D$ a measurable real-valued skew-symmetric matrix in $mathbb{R}^n$ with
entries in $BMO(mathbb{R}^n)$;, i.e., the domain of $sqrt{L},$ is the Sobolev space $dot H^1(mathbb{R}^n)$ in any dimension, with the estimate $|sqrt{L}, f|_2lesssim | abla f|_2$.
We consider nonlinear elastic wave equations generalizing Goldbergs five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses. Using the boundary measurements of the nonl
inear responses, we solve the inverse problem of determining elastic parameters from the displacement-to-traction map.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
