共查询到20条相似文献,搜索用时 31 毫秒
1.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3479-3488
A nonlinear backward heat problem for an infinite strip is considered. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we use the Fourier regularization method to solve the problem. Some sharp estimates of the error between the exact solution and its regularization approximation are given. 相似文献
2.
Habib Ammari Hyeonbae Kang Eunjoo Kim Kaouthar Louati Michael S. Vogelius 《Numerische Mathematik》2008,108(4):501-528
We establish an asymptotic representation formula for the steady state current perturbations caused by internal corrosive
boundary parts of small surface measure. Based on this formula we design a non-iterative method of MUSIC (multiple signal
classification) type for localizing the corrosive parts from voltage-to-current observations. We perform numerical experiments
to test the viability of the algorithm and the results clearly demonstrate that the algorithm works well even in the presence
of relatively high noise ratios.
H. Ammari is partially supported by the Brain Pool Korea Program at Seoul National University, H. Kang is partially supported
by KOSEF grant R01-2006-000-10002-0, E. Kim is supported by BK21 Math. Division at Seoul National University, and M.S. Vogelius
is partially supported by NSF grant DMS-0604999. 相似文献
3.
Asymptotic expansions for currents caused by small interface changes of an electromagnetic inclusion
Habib Zribi 《Applicable analysis》2013,92(1):172-190
We consider solutions to the Helmholtz equation in two dimensions. The aim of this article is to advance the development of high-order asymptotic expansions for boundary perturbations of currents caused by small perturbations of the shape of an inhomogeneity with 𝒞2-boundary. The work represents a natural completion of Ammari et al. [H. Ammari, H. Kang, M. Lim, and H. Zribi, Conductivity interface problems. Part I: Small perturbations of an interface, Trans. Am. Math. Soc. 363 (2010), pp. 2901–2922], where the solution for the Helmholtz equation is represented by a system and the proof of our asymptotic expansion is radically different from Ammari et al. (2010). Our derivation is rigorous and is based on the field expansion method. Its proof relies on layer potential techniques. It plays a key role in developing effective algorithms to determine certain properties of the shape of an inhomogeneity based on boundary measurements. 相似文献
4.
LiShenghong 《高校应用数学学报(英文版)》2000,15(3):297-301
In this paper,the application of the G class of functions in the parabolic class is considered. The regularity of the solution for the first boundary value problem of parabolic equation in divergence form is proved. 相似文献
5.
In this paper we consider two nonlinear elliptic problems driven by the p-Laplacian and having a nonsmooth potential (hemivariational inequalities). The first is an eigenvalue problem and we prove
that if the parameter λ < λ2 = the second eigenvalue of the p-Laplacian, then there exists a nontrivial smooth solution. The second problem is resonant both near zero and near infinity
for the principal eigenvalue of the p-Laplacian. For this problem we prove a multiplicity result. Our approach is variational based on the nonsmooth critical point
theory.
Second author is Corresponding author. 相似文献
6.
In this paper we study the problem of finding a conformal metric with the property that the kth elementary symmetric polynomial of the eigenvalues of its Weyl-Schouten tensor is constant. A new conformal invariant involving maximal volumes is defined, and this invariant is then used in several cases to prove existence of a solution, and compactness of the space of solutions (provided the conformal class admits an admissible metric). In particular, the problem is completely solved in dimension four, and in dimension three if the manifold is not simply connected. 相似文献
7.
Xiaohua Shen 《Journal of Differential Equations》2008,244(11):2836-2869
A novel variational problem is investigated which comes from the study of the Ginzburg-Landau model of superconductivity with impurity inclusion. The feature of this variational problem is that it depends on the impurity set. Some properties of the variational problem are established and an application is given to the Ginzburg-Landau model of superconductivity with impurity inclusion. 相似文献
8.
Shuichi Jimbo Yoshihisa Morita 《Calculus of Variations and Partial Differential Equations》2002,15(3):325-352
We study the Ginzburg-Landau equation with magnetic effect in a thin domain in , where the thickness of the domain is controlled by a parameter . This equation is an Euler equation of a free energy functional and it has trivial solutions that are minimizers of the functional.
In this article we look for a nontrivial stable solution to the equation, that is, a local minimizer of the energy functional.
To prove the existence of such a stable solution in , we consider a reduced problem as and a nondegenerate stable solution to the reduced equation. Applying the standard variational argument, we show that there
exists a stable solution in near the solution to the reduced equation if is sufficiently small. We also present a specific example of a domain which allows a stable vortex solution, that is, a stable
solution with zeros.
Received: 11 May 2001 / Accepted: 11 July 2001 /Published online: 19 October 2001 相似文献
9.
Dongsheng Kang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):682-688
In this paper, a kind of quasilinear elliptic problem is studied, which involves the critical exponent and singular potentials. By the Caffarelli-Kohn-Nirenberg inequality and variational methods, some important properties of the positive solution to the problem are established. 相似文献
10.
《Journal of Differential Equations》2004,198(1):129-148
In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω)?Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω),α)?Lq(P(Ω),β).For the special case p=q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. 相似文献
11.
In this paper parameter-dependent partial differential operators are investigated which satisfy the condition of N-ellipticity with parameter, an ellipticity condition formulated with the use of the Newton polygon. For boundary value problems with general boundary operators we define N-ellipticity including an analogue of the Shapiro-Lopatinskii condition. It is show that the boundary value problem is N-elliptic if and only if an a priori estimate with respect to certain parameter-dependent norms holds. These results are closely connected with singular perturbation theory and lead to uniform estimates, for problems of Vishik-Lyusternik type containing a small parameter.Supported in part by the Deutsche Forschungsgemeinschaft and by Russian Foundation of Fundamental Research, Grant 00-01-00387. 相似文献
12.
Simon N. Chandler-Wilde Peter Monk Martin Thomas 《Journal of Computational and Applied Mathematics》2007
In this paper we study, via variational methods, a boundary value problem for the Helmholtz equation modelling scattering of time harmonic waves by a layer of spatially varying refractive index above an unbounded rough surface on which the field vanishes. In particular, in the 2D case with TE polarization, the boundary value problem models the scattering of time harmonic electromagnetic waves by an inhomogeneous conducting or dielectric layer above a perfectly conducting unbounded rough surface, with the magnetic permeability a fixed positive constant in the medium. Via analysis of an equivalent variational formulation, we show that this problem is well-posed in two important cases: when the frequency is small enough; and when the medium in the layer has some energy absorption. In this latter case we also establish exponential decay of the solution with depth in the layer. An attractive feature is that all constants in our estimates are bounded by explicit functions of the index of refraction and the geometry of the scatterer. 相似文献
13.
The authors investigate the problem of identifying the domainG of a harmonic functionu such that Cauchy data are given on a known portion of the boundary ofG, while a zero Dirichlet condition is specified on the remaining portion of the boundary, which is to be found. Under certain conditions on the domainG, it is shown that the problem reduces to identifying the coefficients of an elliptic equation which, in turn, is converted into the problem of minimizing a functional. Under certain conditions onG, it is shown that the solution, if it exists, is unique. An application is pointed out for the problem of designing a vessel shape that realizes a given plasma shape.This work was completed with a financial support from the National Basic Research in the Natural Sciences. 相似文献
14.
Nikolaos S. Papageorgiou Eugénio M. Rocha Vasile Staicu 《Nonlinear Analysis: Theory, Methods & Applications》2008
We consider a parametric nonlinear elliptic inclusion with a multivalued p-Laplacian-like differential operator and a nonsmooth potential (hemivariational inequality). Using a variational approach based on the nonsmooth critical point theory, we show that for all the values of the parameter in an open half-line, the problem admits at least two nontrivial solutions. Our result extends a recent one by Kristály, Lisei, and Varga [A. Kristály, H. Lisei, C. Varga, Multiple solutions for p-Laplacian type operator, Nonlinear Anal. 68 (5) (2008) 1375–1381]. 相似文献
15.
Gabriele Bonanno Giovanni Molica Bisci Vicenţiu D. Rădulescu 《Nonlinear Analysis: Theory, Methods & Applications》2012
In this paper, we are interested in the existence of infinitely many weak solutions for a non-homogeneous eigenvalue Dirichlet problem. By using variational methods, in an appropriate Orlicz–Sobolev setting, we determine intervals of parameters such that our problem admits either a sequence of non-negative weak solutions strongly converging to zero provided that the non-linearity has a suitable behaviour at zero or an unbounded sequence of non-negative weak solutions if a similar behaviour occurs at infinity. 相似文献
16.
In the present paper we consider the Dirichlet problem in a convex domain for the multidimensional p-Laplace equation with nonlinear source. We prove the existence of the unique continuous viscosity solution under quite general
assumptions on the structure of the source.
Received: 18 January 2006 相似文献
17.
Jorge García-Melián José C. Sabina De Lis Julio D. Rossi 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(5-6):499-525
We deal with positive solutions of Δu = a(x)u
p
in a bounded smooth domain subject to the boundary condition ∂u/∂v = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and only if |∂Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile
of the solution as λ → σ1.
Supported by DGES and FEDER under grant BFM2001-3894 (J. García-Melián and J. Sabina) and ANPCyT PICT No. 03-05009 (J. D.
Rossi). J.D. Rossi is a member of CONICET. 相似文献
18.
Summary For the numerical solution of inverse Helmholtz problems the boundary value problem for a Helmholtz equation with spatially variable wave number has to be solved repeatedly. For large wave numbers this is a challenge. In the paper we reformulate the inverse problem as an initial value problem, and describe a marching scheme for the numerical computation that needs only n2 log n operations on an n × n grid. We derive stability and error estimates for the marching scheme. We show that the marching solution is close to the low-pass filtered true solution. We present numerical examples that demonstrate the efficacy of the marching scheme. 相似文献
19.
Habib Ammari Hyeonbae Kang Eunjoo Kim Hyundae Lee 《Mathematical Methods in the Applied Sciences》2009,32(7):863-874
In this paper we propose an efficient method to reconstruct a small inclusion buried inside a body using the perturbation of modal parameters measured on the boundary of the body. We design a reconstruction algorithm based on the asymptotic expansions of the eigenvalue perturbations obtained by Ammari and Moskow (Math. Meth. Appl. Sci. 2003; 26 :67–75). We then implement this algorithm and demonstrate its viability and limitations. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
20.
We consider a semilinear elliptic Dirichlet problem with jumping nonlinearity and, using variational methods, we show that the number of solutions tends to infinity as the number of jumped eigenvalues tends to infinity. In order to prove this fact, for every positive integer k we prove that, when a parameter is large enough, there exists a solution which presents k interior peaks. We also describe the asymptotic behaviour and the profile of this solution as the parameter tends to infinity. 相似文献