共查询到20条相似文献,搜索用时 31 毫秒
1.
The authors study the inverse problem of recovering damping coefficients for two
coupled hyperbolic PDEs with Neumann boundary conditions by means of an additional
measurement of Dirichlet boundary traces of the two solutions on a suitable, explicit subportion
Γ1 of the boundary Γ, and over a computable time interval T > 0. Under sharp
conditions on Γ0 = ΓnΓ1, T > 0, the uniqueness and stability of the damping coefficients
are established. The proof uses critically the Carleman estimate due to Lasiecka et al. in
2000, together with a convenient tactical route “post-Carleman estimates” suggested by
Isakov in 2006. 相似文献
2.
E. Kengne 《Ukrainian Mathematical Journal》2005,57(8):1334-1340
We investigate the problem of the well-posedness of a boundary-value problem for a system of pseudodifferential equations
of arbitrary order with nonlocal conditions. The equation and boundary conditions contain pseudodifferential operators whose
symbols are defined and continuous in a certain domain H ⊂ ℝ
σ
m
. A criterion for the existence and uniqueness of solutions and for the continuous dependence of the solution on the boundary
function is established.
__________
Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1131 – 1136, August, 2005. 相似文献
3.
Sophia Th. Kyritsi Nikolaos Matzakos Nikolaos Papageorgiou 《Czechoslovak Mathematical Journal》2005,55(3):545-579
In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a
maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator
of the form x ↦ a(x, x′)′. In this problem the maximal monotone term is required to be defined everywhere in the state space ℝN. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ (a(x)x′)′. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential
variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of
solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side. 相似文献
4.
M. A. Berezhnoi 《Ukrainian Mathematical Journal》2009,61(3):361-382
We study the asymptotic behavior of solutions of the problem that describes small motions of a viscous incompressible fluid
filling a domain Ω with a large number of suspended small solid interacting particles concentrated in a small neighborhood
of a certain smooth surface Γ ⊂ Ω. We prove that, under certain conditions, the limit of these solutions satisfies the original equations in the domain Ω\Γ and some averaged boundary conditions (conjugation conditions) on Γ. 相似文献
5.
The asymptotic behavior of solutions to boundary value problems for the Poisson equation is studied in a thick two-level junction
of type 3:2:2 with alternating boundary conditions. The thick junction consists of a cylinder with ε-periodically stringed
thin disks of variable thickness. The disks are divided into two classes depending on their geometric structure and boundary
conditions. We consider problems with alternating Dirichlet and Neumann boundary conditions and also problems with different
alternating Fourier (Neumann) conditions. We study the influence of the boundary conditions on the asymptotic behavior of
solutions as ε → 0. Convergence theorems, in particular, convergence of energy integrals, are proved. Bibliography: 31 titles.
Illustrations: 1 figure. 相似文献
6.
Hui-ling LI & Ming-xin WANG Department of Mathematics Southeast University Nanjing China 《中国科学A辑(英文版)》2007,50(4):590-608
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0. 相似文献
7.
A. V. Shanin 《Journal of Mathematical Sciences》2008,148(5):769-783
The problems of diffraction by a slit or a strip having ideal boundary conditions, and some other problems, can be reduced
to the problem of wave propagation on a multisheet surface by applying the method of reflections. Further simplifications
of the problem can be achieved by applying an embedding formula. As a result, the solution of the problem with a plane wave
incidence becomes expressed in terms of the edge Green’s functions, i.e., in terms of the fields generated by dipole sources
localized at branchpoints of the surface.
The present paper is devoted to finding the edge Green’s functions. For this problem, two sets of differential equations,
namely, the coordinate and spectral equations, are used. The properties of solutions of these equations are studied. Bibliography:
9 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 233–256. 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.
G. I. Shishkin 《Computational Mathematics and Mathematical Physics》2009,49(10):1748-1764
The initial-boundary value problem in a domain on a straight line that is unbounded in x is considered for a singularly perturbed reaction-diffusion parabolic equation. The higher order derivative in the equation
is multiplied by a parameter ɛ2, where ɛ ∈ (0, 1]. The right-hand side of the equation and the initial function grow unboundedly as x → ∞ at a rate of O(x
2). This causes the unbounded growth of the solution at infinity at a rate of O(Ψ(x)), where Ψ(x) = x
2 + 1. The initialboundary function is piecewise smooth. When ɛ is small, a boundary and interior layers appear, respectively,
in a neighborhood of the lateral part of the boundary and in a neighborhood of the characteristics of the reduced equation
passing through the discontinuity points of the initial function. In the problem under examination, the error of the grid
solution grows unboundedly in the maximum norm as x → ∞ even for smooth solutions when ɛ is fixed. In this paper, the proximity of solutions of the initial-boundary value problem
and its grid approximations is considered in the weighted maximum norm ∥·∥
w
with the weighting function Ψ−1(x); in this norm, the solution of the initial-boundary value problem is ɛ-uniformly bounded. Using the method of special grids
that condense in a neighborhood of the boundary layer or in neighborhoods of the boundary and interior layers, special finite
difference schemes are constructed and studied that converge ɛ-uniformly in the weighted norm. It is shown that the convergence
rate considerably depends on the type of nonsmoothness in the initial-boundary conditions. Grid approximations of the Cauchy
problem with the right-hand side and the initial function growing as O(Ψ(x)) that converge ɛ-uniformly in the weighted norm are also considered. 相似文献
10.
V. V. Kamotskii 《Journal of Mathematical Sciences》2006,138(2):5514-5523
The problem of scattering on two wedges with ideal boundary conditions is considered. A uniqueness theorem is proved. Under
a certain geometric assumption on the “narrowness” of the wedges, the existence of solutions of scattering problems of plane
and cylindrical waves is proved by applying the spectral function method. Bibliography: 3 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 61–76. 相似文献
11.
Boundary value problems for the Poisson equation are considered in a multilevel thick junction consisting of a junction body
and a lot of alternating thin rectangles of two levels depending on their lengths. Rectangles of the first level have a finite
length, whereas rectangles of the second level have a length ε
α
, 0 < α < 1, where ε is the alternation period. On the boundary of thin rectangles, an inhomogeneous Neumann boundary condition involving additional
perturbation parameters is imposed. We prove convergence theorems for solutions and energy integrals. Regarding the convergence
of solutions of the original problem to solutions of the homogenized problem, we establish some (auxiliary) estimates necessary
for obtaining the convergence rate. Bibliography: 48 titles. Illustrations: 3 figures.
Dedicated to Nina Nikolaevna Uraltseva
Translated from Problemy Matematicheskogo Analiza, 40, May 2009, pp. 113–132. 相似文献
12.
C. A. Stuart 《Milan Journal of Mathematics》2011,79(1):327-341
For a class of second order quasilinear elliptic equations we establish the existence of two non–negative weak solutions of
the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C
1–functional on H01(W){H_0^1(\Omega)}. One solution is a local minimum and the other is of mountain pass type. 相似文献
13.
Leonid S. Frank 《Annali di Matematica Pura ed Applicata》1979,119(1):41-113
Summary We consider general boundary value problems with small parameter ɛ in the operator and boundary conditions. Both the perturbed
and reduced operators are supposed to be elliptic. We point outnecessary andsufficient conditions of Shapiro-Lopatinsky type for the singularly perturbed problem to be coercive, i.e. for a two-sided a priori
estimate to hold for its solutions uniformly with respect to ɛ.
Entrata in Redazione il 6 luglio 1977. 相似文献
14.
This paper describes a spectral representation of solutions of self-adjoint elliptic problems with immersed interfaces. The
interface is assumed to be a simple non-self-intersecting closed curve that obeys some weak regularity conditions. The problem
is decomposed into two problems, one with zero interface data and the other with zero exterior boundary data. The problem
with zero interface data is solved by standard spectral methods. The problem with non-zero interface data is solved by introducing
an interface space H
Γ(Ω) and constructing an orthonormal basis of this space. This basis is constructed using a special class of orthogonal eigenfunctions
analogously to the methods used for standard trace spaces by Auchmuty (SIAM J. Math. Anal. 38, 894–915, 2006). Analytical and numerical approximations of these eigenfunctions are described and some simulations are presented. 相似文献
15.
Wei-hua Yang 《应用数学学报(英文版)》2006,22(4):687-702
In this paper, we consider the Neumann boundary value problem for a system of two elliptic equations involving the critical Sobolev exponents. By means of blowing-up method, we obtain behavior of positives with low energy and asymptotic behavior of positive solutions with minimum energy as the parameters λ,μ→∞. 相似文献
16.
Mustafa Kandemir Oktay Mukhtarov Yakov Yakubov 《Mediterranean Journal of Mathematics》2009,6(3):317-338
In this study, a Birkhoff-irregular boundary value problem for linear ordinary differential equations of the second order
with discontinuous coefficients and the spectral parameter has been considered. Therefore, at the discontinuous point, two
additional boundary conditions (called transmission conditions) have been added to the boundary conditions. The eigenvalue
parameter is of the second degree in the differential equation and of the first degree in a boundary condition. The equation
contains an abstract linear operator which is (usually) unbounded in the space Lq(−1, 1). Isomorphism and coerciveness with defects 1 and 2 are proved for this problem. The case of the biharmonic equation
is also studied. 相似文献
17.
Yeping Li 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,13(2):187-211
In this paper, a one-dimensional nonisentropic hydrodynamic model for semiconductors with non-constant lattice temperature
is studied. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum
equation, is determined by the coupled Poisson equation. The existence and uniqueness of the corresponding stationary solutions
are investigated carefully under proper conditions. Then, global existence of the smooth solutions for the Cauchy problem
with initial data, which are perturbations of stationary solutions, is established. It is shown that these smooth solutions
tend to the stationary solutions exponentially fast as t → ∞.
相似文献
18.
We consider a boundary-value problem for the second-order elliptic differential operator with rapidly oscillating coefficients
in a domain Ω
ε
that is ε-periodically perforated by small holes. The holes are split into two ε-periodic sets depending on the boundary interaction via their boundary surfaces. Therefore, two different nonlinear boundary
conditions σ
ε
(u
ε
) + εκ
m
(u
ε
) = εg
ε
(m)
, m = 1, 2, are given on the corresponding boundaries of the small holes. The asymptotic analysis of this problem is performed as ε → 0, namely, the convergence theorem for both the solution and the energy integral is proved without using an extension operator,
asymptotic approximations for the solution and the energy integral are constructed, and the corresponding approximation error
estimates are obtained. 相似文献
19.
Daniel Michelson 《Journal d'Analyse Mathématique》1989,53(1):1-138
The general problem studied has as a prototype the full non-linear Navier-Stokes equations for a slightly viscous compressible
fluid including the heat transfer. The boundaries are of inflow-outflow type, i.e. non-characteristic, and the boundary conditions
are the most general ones with any order of derivatives. It is assumed that the uniform Lopatinsky condition is satisfied.
The goal is to prove uniform existence and boundedness of solution as the viscosity tends to zero and to justify the boundary
layer asymptotics. The paper consists of two parts. In Part I the linear problem is studied. Here, uniform lower and higher
order tangential estimates are derived and the existence of a solution is proved. The higher order estimates depend on the
smoothness of coefficients; however this smoothness does not exceed the smoothness of the solution. In Part II the quasilinear
problem is studied. It is assumed that for zero viscosity the overall initial-boundary value problem has a smooth solutionu
0 in a time interval 0≦t≦T
0. As a result the boundary laye, is weak and is uniformlyC
1 bounded. This makes the linear theory applicable. an iteration scheme is set and proved to converge to the viscous solution.
The convergence takes place for small viscosity and over the original time interval 0≦t≦T
0. 相似文献
20.
We construct weak solutions to parabolic systems of the variational flow type related to a quadratic functional with the initial
and boundary data from a suitable Sobolev space and subjected to two-sided conditions. We present an approach based on Rothe’s
method. It is applicable to solving the Cauchy problem and initial boundary-value problem for many types of equations. Bibliography:
12 titles.
Translated fromZapiski Nauchnykh Seminarov, POMI, Vol. 243, 1997, pp. 324–337. 相似文献