共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the inverse problem of recovering an interior interface from a boundary measurement in an elliptic boundary value
problem arising from a semiconductor transistor model. We set up a nonlinear least-squares formulation for solving the inverse
problem, and establish the necessary derivatives with respect to the interface. We then propose both the Gauss–Newton iterative
method and the conjugate gradient method for the least-squares problem, and present implementation of these methods using
integral equations. 相似文献
2.
Haïm Brezis Jean Van Schaftingen 《Calculus of Variations and Partial Differential Equations》2007,30(3):369-388
We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions
and L
1–data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div–curl and Hodge
systems. 相似文献
3.
A. F. Tedeev 《Ukrainian Mathematical Journal》2006,58(2):304-317
We study the behavior of the total mass of the solution of Neumann problem for a broad class of degenerate parabolic equations
with damping in spaces with noncompact boundary. New critical indices for the investigated problem are determined.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 2, pp. 272–282, February, 2006. 相似文献
4.
J. Chabrowski 《Annali di Matematica Pura ed Applicata》2007,186(4):703-719
In this paper we investigate the solvability of the nonlinear Neumann problem (1.1) with indefinite weight functions and a
critical Hardy–Sobolev nonlinearity. We examine the common effect of the shape of the graph of a weight function and the mean
curvature of the boundary on the existence of solutions of problem (1.1). We also investigate the regularity of solutions.
相似文献
5.
I. V. Nezhinskaya 《Journal of Mathematical Sciences》2006,132(4):428-440
We consider the Neumann boundary value problem for the class of (p,q)-nonlinear elliptic equations. The numbers p and q, 2
⩽ p < q, characterize the power growth with respect to the gradient of eigenvalues of the leading matrix of the equation.
An a priori estimate for the maximum of the modulus of the gradient of the solution is obtained in a neighborhood of the boundary
of the domain for some interval of p and q. Bibliography: 5 titles.
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Translated from Problemy Matematicheskogo Analiza, No. 31, 2005, pp. 47–57. 相似文献
6.
This article gives a complex analysis lighting on the problem which consists in restoring a bordered connected riemaniann
surface from its boundary and its Dirichlet–Neumann operator. The three aspects of this problem, unicity, reconstruction and
characterization are approached.
Received: May 2005 Revision: October 2005 Accepted: October 2005 相似文献
7.
Mahdi Boukrouche 《Mathematical Methods in the Applied Sciences》1994,17(10):765-785
We study a non-linear problem in pressure saturation modelling of a free boundary problem, arising in self-lubricating bearings, with Neumann boundary conditions for the pressure and a non-local constraint on the saturation variable, which indeed is a Lagrange multiplier. We prove an existence theorem by introducing an artificial time dependence and using the pseudo-characteristics discretization method and semi-coercive variational inequalities. 相似文献
8.
Asymptotic representations of solutions to the boundary-value problems of elasticity theory are studied in domains with parabolic
exit at infinity (or in bounded domains with singularities like polynomial zero sharpness). The procedure of derivating a
formal asymptotic expansion looks like the algorithm of asymptotic analysis in domains. Under the Dirichlet conditions (displacements
are prescribed on the boundary of a domain), it is not hard to justify the power asymptotic series. It follows from the theorem
on the unique solvability of the problem in spaces of the type L2 containing degrees of distance r=|x| as weight multipliers. For the Neumann conditions (stresses are prescribed on the boundary
of a domain) an asymptotic expansion is justified by introducing the Eiry function Φ transforming the Lamé system to the biharmonic
equation. Due to the appearance of the Dirichlet condition on Φ, the study of the asymptotic behavior of a solution to the
last problem is simplified. The existence theorems and conditions for solvability of the “elastic” Neumann problem are presented.
These results are based on the weighted Korn inequality. Bibliography: 29 titles.
Translated fromProblemy Matematicheskogo Analiza. No. 15, 1995, pp. 162–200 相似文献
9.
《Applied Mathematics Letters》2001,14(6):753-758
This note deals with the low-frequency time-harmonic Maxwell equations for a heterogeneous media in bidimensional bounded domains. We propose a three step method to solve this problem. First, we construct an extension of the boundary data solving a scalar Neumann problem for the Laplace operator. Second, we solve a problem in the conductor with an unusual boundary condition of nonlocal type. Third, we solve a boundary value problem in the insulator using the solution calculated in the conductor. Also, this third problem can be reduced to a Neumann problem for the Laplace operator. 相似文献
10.
G. A. Chechkin 《Journal of Mathematical Sciences》2006,135(6):3485-3521
We study the asymptotic behavior of eigenelements of boundary value problems in a domain Ω ⊂ ℝd, d ⩾ 3, with rapidly alternating type of boundary conditions. The density is equal to 1 outside tiny domains and is equal
to ε−m inside them, where ε is a small parameter. These domains (concentrated masses) of diameter εa are located on the boundary
at a positive distance of order O(ε) from each other, where a = const. The Dirichlet boundary condition is on parts of ∂Ω that are tangent to concentrated masses, and the Neumann boundary condition
is stated outside concentrated masses. We construct the limit (homogenized) operator, prove the convergence of eigenelements
of the original problem to the eigenelements of the limit (homogenized) problem in the case m ⩾ 2, and estimate the difference
between the eigenelements. Bibliography: 79 titles. Illustrations: 4 figures.
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Translated from Problemy Matematicheskogo Analiza, No. 32, 2006, pp. 45–75. 相似文献
11.
An asymptotic expansion of the solution to the Neumann problem for a second-order equation in a thin domain with peak-like
edge is constructed and justified. Owing to the sharpness of the edge, the procedure of dimension reduction leads to a degenerate
limit equation on the longitudinal cross-section of the domain and a solution has irregular behavior near the boundary. Bibliography:
20 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 193–219. 相似文献
12.
Francesca Bucci 《Journal of Evolution Equations》2007,7(3):387-414
We consider a class of structural acoustics models with thermoelastic flexible wall. More precisely, the PDE system consists
of a wave equation (within an acoustic chamber) which is coupled to a system of thermoelastic plate equations with rotational
inertia; the coupling is strong as it is accomplished via boundary terms. Moreover, the system is subject to boundary thermal
control. We show that—under three different sets of coupled (mechanical/thermal) boundary conditions—the overall coupled system
inherits some specific regularity properties of its thermoelastic component, as it satisfies the same singular estimates recently established for the thermoelastic system alone. These regularity estimates are of central importance for (i) well-posedness
of Differential and Algebraic Riccati equations arising in the associated optimal control problems, and (ii) existence of
solutions to the semilinear initial/boundary value problem under nonlinear boundary conditions. The proof given uses as a critical ingredient a sharp trace theorem pertaining to second-order hyperbolic
equations with Neumann boundary data. 相似文献
13.
A. A. Solov'ev 《Mathematical Notes》1996,59(6):637-645
The boundary equations of the logarithmic potential theory corresponding to the interior Dirichlet problem and the exterior
Neumann problem for a plane domain with a cusp on the boundary are studied. Solvability theorems are proved for these integral
equations in the spacesL
p.
Translated fromMatematicheskie Zametki, Vol. 59, No. 6, pp. 881–892, June, 1996. 相似文献
14.
In this paper, we address the problem of the existence of superconvergence points of approximate solutions, obtained from
the Generalized Finite Element Method (GFEM), of a Neumann elliptic boundary value problem. GFEM is a Galerkin method that
uses non-polynomial shape functions, and was developed in (Babuška et al. in SIAM J Numer Anal 31, 945–981, 1994; Babuška
et al. in Int J Numer Meth Eng 40, 727–758, 1997; Melenk and Babuška in Comput Methods Appl Mech Eng 139, 289–314, 1996).
In particular, we show that the superconvergence points for the gradient of the approximate solution are the zeros of a system
of non-linear equations; this system does not depend on the solution of the boundary value problem. For approximate solutions
with second derivatives, we have also characterized the superconvergence points of the second derivatives of the approximate
solution as the roots of a system of non-linear equations. We note that smooth generalized finite element approximation is
easy to construct.
I. Babuška’s research was partially supported by NSF Grant # DMS-0341982 and ONR Grant # N00014-99-1-0724.
U. Banerjee’s research was partially supported by NSF Grant # DMS-0341899.
J. E. Osborn’s research was supported by NSF Grant # DMS-0341982. 相似文献
15.
In the first part of the paper, we give a satisfactory definition of the Stokes operator in Lipschitz domains in
\mathbbRn {\mathbb{R}^n} when boundary conditions of Neumann type are considered. We then proceed to establish optimal global Sobolev regularity results
for vector fields in the domains of fractional powers of this Neumann–Stokes operator. Finally, we study the existence, regularity,
and uniqueness of mild solutions of the Navier–Stokes system with Neumann boundary conditions. Bibliography: 43 titles. Illustrations:
2 figures. 相似文献
16.
Georgios E. Zouraris 《Numerische Mathematik》1997,77(1):123-142
Summary. We analyze a class of algebraically stable Runge–Kutta/standard Galerkin methods for inhomogeneous linear parabolic equations,
with time–dependent coefficients, under Neumann boundary conditions, and derive an error bound of provided is bounded.
Received June 25, 1994 / Revised version received February 26, 1996 相似文献
17.
We consider a simple reaction-diffusion system exhibiting Turing’s diffusion driven instability if supplemented with classical
homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral
condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially
non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential operator,
and a variational approach is used in a certain non-direct way. 相似文献
18.
In this paper we propose and analyse numerical methods for the approximation of the solution of Helmholtz transmission problems
in the half plane. The problems we deal with arise from the study of some models in photothermal science. The solutions to
the problem are represented as single layer potentials and an equivalent system of boundary integral equations is derived.
We then give abstract necessary and sufficient conditions for convergence of Petrov–Galerkin discretizations of the boundary
integral system and show for three different cases that these conditions are satisfied. We extend the results to other situations
not related to thermal science and to non-smooth interfaces. Finally, we propose a simple full discretization of a Petrov–Galerkin
scheme with periodic spline spaces and show some numerical experiments. 相似文献
19.
This paper is concerned with fast spectral-Galerkin Jacobi algorithms for solving one- and two-dimensional elliptic equations
with homogeneous and nonhomogeneous Neumann boundary conditions. The paper extends the algorithms proposed by Shen (SIAM J
Sci Comput 15:1489–1505, 1994) and Auteri et al. (J Comput Phys 185:427–444, 2003), based on Legendre polynomials, to Jacobi polynomials with arbitrary α and β. The key to the efficiency of our algorithms is to construct appropriate basis functions with zero slope at the endpoints,
which lead to systems with sparse matrices for the discrete variational formulations. The direct solution algorithm developed
for the homogeneous Neumann problem in two-dimensions relies upon a tensor product process. Nonhomogeneous Neumann data are
accounted for by means of a lifting. Numerical results indicating the high accuracy and effectiveness of these algorithms
are presented. 相似文献
20.
Vern I. Paulsen 《Journal of Functional Analysis》2008,255(1):120-132
In these notes we develop a link between the Kadison-Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique extension is related to certain dynamical properties of the state. We prove that if any state corresponding to a minimal idempotent point extends uniquely to the von Neumann algebra of the group, then every state extends uniquely to the von Neumann algebra of the group. We prove that if any state arising in the Kadison-Singer problem has a unique extension, then the injective envelope of a C*-crossed product algebra associated with the state necessarily contains the full von Neumann algebra of the group. We prove that this latter property holds for states arising from rare ultrafilters and δ-stable ultrafilters, independent, of the group action and also for states corresponding to non-recurrent points in the corona of the group. 相似文献