共查询到20条相似文献,搜索用时 15 毫秒
1.
Giovanni Alessandrini 《Applicable analysis》2013,92(1-3):153-172
We consider the problem of determining the scalar coefficient γ in the elliptic equation div(γ grad u) = 0 in ω when, for every Dirichlet datum u = ? on ?ω , the Neumann datum γ(?/ ? n)u = ∧.γ? is known. We prove a continuous dependence result 相似文献
2.
Luca Rondi 《Transactions of the American Mathematical Society》2003,355(1):213-239
We consider the inverse problem of determining shape and location of sound-soft defects inside a known planar inhomogeneous and anisotropic medium through acoustic imaging at low frequency. In order to determine the defects, we perform acoustic boundary measurements, with prescribed boundary conditions of different types. We prove that at most two, suitably chosen, measurements allow us to uniquely determine multiple defects under minimal regularity assumptions on the defects and the medium containing them. Finally, we treat applications of these results to the case of inverse scattering.
3.
《Mathematical Methods in the Applied Sciences》2018,41(12):4602-4611
We consider the inverse problem of detecting an inclusion in conductor through electrostatic measurements taken on the boundary. We analyze in particular the stability issue showing that the solution depends from the available data with a rate of continuity of logarithmic type. 相似文献
4.
Masaru Ikehata 《偏微分方程通讯》2013,38(7-8):1459-1474
We give a formula for the reconstruction of the shape of the unknown inclusion by means of the Dirichlet to Neumann map. 相似文献
5.
We consider (in two-dimensional Euclidean space) the scattering of a plane, time-harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacle D lying completely outside of the inhomogeneous medium. We show that one may determine the shape of D and the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques. By assuming a priori that the functions which determine the shape of D and the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far field data. 相似文献
6.
By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
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8.
《Applied Mathematics Letters》2000,13(1):71-76
We study the nonlinear boundary stabilization of an inhomogeneous and anisotropic thermoelasticity system. We generalize a result of Rivera-Oliveira [1] to the nonlinear case. Our main tool is the use of the perturbed energy functional introduced by Komornik-Zuazua [2]. 相似文献
9.
In [2], A. P. Caldéron posed the following question: can one determine the heat conductivity of an object from static temperature and heat flux measurements at the boundary? We show that such measurements uniquely determine the conductivity and all of its derivatives at the boundary. 相似文献
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In this paper, we consider the steady MHD equations with inhomogeneous boundary conditions for the velocity and the tangential component of the magnetic field. Using a new construction of the magnetic lifting, we obtain existence of weak solutions under sharp assumption on boundary data for the magnetic field. 相似文献
12.
Ralph Ennenbach 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1994,45(3):399-413
We give eigenvalue inclusion theorems allowing the computation of both-sided Stekloff-eigenvalue bounds from a given approximate eigenpair. We demonstrate in numerical examples the possibility to get close bounds for even higher eigenvalues using the boundary collocation method. A good choice for trial functions are singularity functions allowing a control for the numerical stability and—in theory—an eigenvalue inclusion in an arbitrary small interval.The inclusion theorems may be interpreted as a priori norm inequalities, too.
Zusammenfassung Wir stellen Eigenwerteinschlußsätze vor, welche die Berechnung beiderseitiger Eigenwertschranken in Abhängigkeit von vorgelegten Näherungseigenpaaren gestatten. Wir demonstrieren an numerischen Beispielen, daß es mit dem Kollokationsverfahren möglich ist, sehr gute Einschlüsse selbst höherer Eigenwerte zu erhalten. Als Ansatzfunktionen bewähren sich Singularitätenfunktionen, welche eine Steuerbarkeit der numerischen Stabilität ermöglichen. Zudem erlauben diese Funktionen in der Theorie einen Einschluß in beliebiger Güte.Die Einschlußsätze können auch als a priori Norm-Ungleichungen angesehen werden.相似文献
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In this study, an effective singular boundary method (SBM) in conjunction with the recursive multiple reciprocity method (MRM) is developed and validated for inhomogeneous problems. It avoids the inner nodes or domain discretizations to evaluate the particular solution, and preserves the boundary-only property of the SBM. Rather than using only polyharmonic operators in the traditional MRM, a recursive MRM is proposed to annihilate source terms with different partial differential operators recursively. Nevertheless, high-order fundamental solutions are involved in the recursive MRM. The absence of the origin intensity factors of higher order fundamental solutions is a major bottleneck in applying the SBM. In order to remedy this difficulty, the origin intensity factors of higher order fundamental solutions are derived with simple formulas. Numerical examples are presented to illustrate the accuracy and efficiency of the proposed method. 相似文献
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16.
We consider the nonlinear problem of inhomogeneous Allen–Cahn equation where Ω is a bounded domain in with smooth boundary, ? is a small positive parameter, ν denotes the unit outward normal of ?Ω, V is a positive smooth function on . Let Γ be a curve intersecting orthogonally with ?Ω at exactly two points and dividing Ω into two parts. Moreover, Γ satisfies stationary and non-degenerate conditions with respect to the functional . We can prove that there exists a solution such that: as , approaches +1 in one part of Ω, while tends to ?1 in the other part, except a small neighborhood of Γ. 相似文献
17.
An approach to inverse problems based on the boundary control theory is developed. The dynamic problem to recover a density
of an inhomogeneous string via its free endopoint oscillations generated by an instantaneous force source is proposed. The
problem is to determine the coefficient ρ(x)>0 in the equation ρ(x)utt(x, t)−uxx(x, t)=0(x, t>0) with the conditions u|<0=0, ux(0, t)=δ(t) by using a known function (response) u(0, t)=r(t) (t>0). The authors propose an algorithm based upon the approach
and demonstrate its numerical efficiency in the test problems including those for nonmonotone ρ(x)'s. Bibliography: 12 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 37–49, 1990.
Translated by T. N. Surkova. 相似文献
18.
V. A. Il’in 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):97-105
The process of damping oscillations of a rod consisting of two dissimilar segments and fixed at one end is considered. The damping is carried out by means of a boundary control at the other end of the rod. 相似文献
19.
X-ray tomographic determination of the chemical composition and structure of an inhomogeneous medium
V. G. Nazarov 《Computational Mathematics and Mathematical Physics》2007,47(8):1358-1367
The chemical composition of an inhomogeneous body consisting of several homogeneous parts is determined by x-ray tomography. At the first stage, an indicator of inhomogeneities is used to determine the internal structure of the body. Next, under certain additional assumptions about the properties of the parts, a method is proposed for partial or complete determination of the chemical composition of each part as based on the results of the previous stage. Mathematically, the problem is reduced to solving the radiative transfer equation and systems of linear algebraic equations. Numerical experiments are performed via computer simulation. The numerical results are illustrated by graphs and tomograms. 相似文献
20.
《Journal of Applied Mathematics and Mechanics》1999,63(4):617-625
The problem of the constructive determination of the natural frequencies and modes of oscillations of distributed systems with substantially varying parameters is investigated. Unlike the classical case, the self-adjoint boundary-value problem allows of an arbitrary non-linear dependence of the coefficients of the equation on a numerical parameter, the eigenvalues of which are required to be obtained. An original numerical-analytic method is developed for a highly accurate construction of the desired solution. The computational efficiency of the algorithm, which possesses the property of accelerated (quadratic) convergence, is illustrated by the calculation of model examples. The approach can be extended to other classes of generalized problems of determining the critical values of the parameters and the forms corresponding to them, in particular, to the problem of the loss of stability of elastic systems with variable stiffnesses and inertial and force characteristics. A highly accurate solution of the classical Prandtl problem of determining the critical force which leads to lateral buckling of a long homogeneous cantilever beam is constructed, taking its weight into account. 相似文献