共查询到20条相似文献,搜索用时 15 毫秒
1.
Robert Dalmasso 《Mathematische Annalen》2000,316(4):771-792
We consider the following elliptic boundary value problem: on , u = 0 on where is a smooth bounded planar domain. We show that for a large class of domains and for any such that is not identically constant there exist at most finitely many different pairs of coefficients such that the problem has a solution with the normal flux on .
Received: 4 February 1999 相似文献
2.
In this article, we consider nonstationary Maxwell's equations in an anisotropic medium in the (x 1,?x 2,?x 3)-space, where equations of the divergences of electric and magnetic flux densities are also unknown. Then we discuss an inverse problem of determining the x 3-independent components of the electric current density from observations on the plane x 3?=?0 over a time interval. Our main aim is, study conditional stability in the inverse problem provided the permittivity and the permeability are independent of x 3. The main tool is a new Carleman estimate. 相似文献
3.
ABSTRACT We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with homogeneous initial and Dirichlet data. 相似文献
4.
A. Boumenir 《Applicable analysis》2013,92(3):221-228
We propose an algorithm for the recovery of a potential from the knowledge of the eigenvalues of the Laplacian operator and the traces of its eigenfunctions. This inverse spectral problem is solved by recasting the operator as an infinite matrix and using transition matrices together with spectral projections on the boundary. 相似文献
5.
Michael V. Klibanov Vladimir G. Kamburg 《Mathematical Methods in the Applied Sciences》2016,39(4):930-940
A coefficient inverse problem for a parabolic equation is considered. Using a Carleman weight function, a globally strictly convex cost functional is constructed for this problem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
6.
Juan Manfredi Arshak Petrosyan Henrik Shahgholian 《Calculus of Variations and Partial Differential Equations》2002,14(3):359-384
We consider a free boundary problem for the p-Laplacian
describing nonlinear potential flow past a convex profile K with prescribed pressure on the free stream line. The main purpose of this paper is to study the limit as of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the -Laplacian
in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case the limit is given by the distance function.
Received: 10 October 2000 / Accepted: 23 February 2001 / Published online: 19 October 2001 相似文献
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9.
Maurizio Grasselli 《Numerical Functional Analysis & Optimization》2013,34(3-4):311-323
The evolution of population densities of two interacting species in presence of diffusion phenomena is governed by a system of semilinear Volterra integrodifferential parabolic equations. In this system there are time convolution integrals, accounting for past history effects, which are essentially characterized by kernels depending on time only. These delay kernels can be viewed as entries of a 2x2 matrix K. The inverse problem of determining K via suitable population measurements is analyzed. 相似文献
10.
We consider an inverse boundary value problem for identifying the inclusion inside a known anisotropic conductive medium. We give a reconstruction procedure for identifying the inclusion from the Dirichlet–Neumann map or the Neumann–Dirichlet map associated with the mixed type boundary condition. 相似文献
11.
Concerning the obstacle-problem-like equation
, where + > 0 and – > 0, we give a complete characterization of all global two-phase solutions with quadratic growth both at 0 and infinity. 相似文献
12.
Shitao Liu 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2647-2662
We consider an inverse problem of determining a source term for a structural acoustic partial differential equation (PDE) model that is comprised of a two- or a three-dimensional interior acoustic wave equation coupled to an elastic plate equation. The coupling takes place across a boundary interface. For this PDE system, we obtain uniqueness and stability estimates for the source term from a single measurement of boundary values of the “structure” (acceleration of the elastic plate). The proof of uniqueness is based on a Carleman estimate (first version) of the wave problem within the chamber. The proof of stability relies on three main points: (i) a more refined Carleman estimate (second version) and its resulting implication, a continuous observability-type estimate; (ii) a compactness/uniqueness argument; (iii) an operator theoretic approach for obtaining the needed regularity in terms of the initial conditions. 相似文献
13.
Pavol Quittner 《Mathematische Annalen》2001,320(2):299-305
We prove universal a priori estimates of global positive solutions of the parabolic problem in , on . Here is a bounded domain in , , and p < 5 if n=3.
Received April 6, 2000 / Accepted September 21, 2000 / Published online February 5, 2001 相似文献
14.
We consider an inverse problem of determining a viscosity coefficient in the Navier-Stokes equation by observation data in a neighborhood of the boundary. We prove the Lipschitz stability by the Carleman estimates in Sobolev spaces of negative order. 相似文献
15.
We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical
case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.
While the only small self-similar solution in the strong
space is the null solution, infinitely many self-similar solutions do exist in weak-
spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained
in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained. 相似文献
16.
Antoine Lejay 《Probability Theory and Related Fields》2001,120(2):255-276
The probabilistic machinery (Central Limit Theorem, Feynman-Kac formula and Girsanov Theorem) is used to study the homogenization
property for PDE with second-order partial differential operator in divergence-form whose coefficients are stationary, ergodic
random fields. Furthermore, we use the theory of Dirichlet forms, so that the only conditions required on the coefficients
are non-degeneracy and boundedness.
Received: 27 August 1999 / Revised version: 27 October 2000 / Published online: 26 April 2001 相似文献
17.
Bin Wu 《Mathematical Methods in the Applied Sciences》2012,35(4):427-437
In this paper, we establish a Carleman estimate for a strongly damped wave equation in order to solve a coefficient inverse problems of retrieving a stationary potential from a single time‐dependent Neumann boundary measurement on a suitable part of the boundary. This coefficient inverse problem is for a strongly damped wave equation. We prove the uniqueness and the local stability results for this inverse problem. The proof of the results relies on Carleman estimate and a certain energy estimates for hyperbolic equation with strongly damped term. Moreover, this method could be used for a similar inverse problem for an integro‐differential equation with hyperbolic memory kernel. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
18.
For 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 establish the conditional stability in Sobolev's norm of the displacement by means of measurements in an arbitrary subdomain or measurements of surface displacement and stress on an arbitrary subboundary. Finally by the Carleman estimate, we prove the uniqueness and conditional stability for an inverse problem of determining a source term by a single interior measurement. 相似文献
19.
Michael V. Klibanov Sergey E. Pamyatnykh 《Journal of Mathematical Analysis and Applications》2008,343(1):352-365
A coefficient inverse problem for the non-stationary single-speed transport equation for t∈(0,T) with the lateral boundary data and initial condition at t=0 is considered. Global uniqueness result is obtained by the method of Carleman estimates. 相似文献
20.
Nicolas Valdivia 《Applicable analysis》2013,92(8):825-851
We consider the uniqueness of the inverse obstacle scattering with conductive boundary conditions. This work is based on the original idea of Isakov for transmission boundary conditions, which utilize the solvability of the direct problem, orthogonality relations, approximations to solution of the direct problem and singular solutions. The methodology used is constructive and allows an extension to more general conditions and numerical methods. 相似文献