共查询到20条相似文献,搜索用时 31 毫秒
1.
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients. 相似文献
2.
This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained. 相似文献
3.
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown
coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible
coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients.
The existence of quasisolutions of the inverse problems is obtained. 相似文献
4.
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained. 相似文献
5.
A. M. Denisov 《Differential Equations》2009,45(11):1577-1587
We consider two inverse coefficient problems for a quasilinear hyperbolic equation, where the additional information used
for finding the coefficients is the values of the solution on some curve. (This corresponds to measurements performed at a
moving observation point.) The unknown coefficient depends on the space variable in the first inverse problem and on the solution
of the equation in the second inverse problem. We prove theorems of uniqueness of solution to the inverse problems. 相似文献
6.
This study is related to inverse coefficient problems for a nonlinear parabolic variational inequality with an unknown leading coefficient in the equation for the gradient of the solution. An inverse method, involving minimization of a least-squares cost functional, is developed to identify the unknown coefficient. It is proved that the solution of the corresponding direct problem depends continuously on the coefficient. On the basis of this, the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients. 相似文献
7.
The goal of this work is to determine appropriate domain and range of the map from the coefficients to the solutions of the wave equation for which its linearization or formal derivative is bounded and the properties of the coefficients on which the bound depends.Such information is indispensable in the study of the inverse (coefficient identification) problem vio smooth optimization methods. The main result of this paper is an explicit microlocal Sobolev estimate for the linearized forward map. In view of results of Rakesh [19] for the smooth coefficient case, the order of our regularity result is optimal. Our proof is based on the method of nonsmooth microlocal analysis, in particular various results on propagation of singularities, the method of progressing wave expansions, microlocal study of solutions of the transport equations, study of conormal properties of the fundamental solution, and a duality technique. 相似文献
8.
《Journal de Mathématiques Pures et Appliquées》2006,85(2):193-224
We study the global stability in determination of a coefficient in an acoustic equation from data of the solution in a subboundary over a time interval. Providing regular initial data and values of coefficients in a neighbourhood of the boundary, without any assumption on an observation subboundary, we prove the logarithmic stability estimate in the inverse problem with a single measurement. Moreover the exponent in the stability estimate depends on the regularity of initial data. 相似文献
9.
Ping CHEN~ 《中国科学A辑(英文版)》2007,50(11):1597-1610
The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1-dimensional bounded Lipschitzian function of the state or the time only.There is no previous work for the nonparametric estimation of time-dependent diffusion models where the diffusion coefficient depends on both the state and the time.This paper introduces and studies a wavelet estimation of the time-dependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz function.Using the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the L~r convergence rate.A strong consistency of the estimate is established.With this result one can estimate the time-dependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability measure.For example, in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure. 相似文献
10.
For a parabolic equation, we consider inverse problems of reconstructing a coefficient that depends on the space variables
alone. The first problem is to find a lower-order coefficient c(x) multiplying u(x, t), and the second problem is to find the coefficient a(x) multiplying Δu. As additional information, the integral of the solution with respect to time with some weight function is given. The coefficients
of the equation depend both on time and on the space variables. We obtain sufficient conditions for the existence of generalized
solutions of our problems; moreover, for the first problem, we also prove uniqueness and construct an iterative sequence that
converges to the desired coefficient almost everywhere in the domain. We present examples of input data of these problems
for which the assumptions of our theorems are necessarily true. 相似文献
11.
Todd Kapitula Elizabeth Hibma Hwa-Pyeong Kim Jonathan Timkovich 《Linear algebra and its applications》2013
There is a well-established instability index theory for linear and quadratic matrix polynomials for which the coefficient matrices are Hermitian and skew-Hermitian. This theory relates the number of negative directions for the matrix coefficients which are Hermitian to the total number of unstable eigenvalues for the polynomial. Herein we extend the theory to ?-even matrix polynomials of any finite degree. In particular, unlike previously known cases we show that the instability index depends upon the size of the matrices when the degree of the polynomial is greater than two. We also consider Hermitian matrix polynomials, and derive an index which counts the number of eigenvalues with nonpositive imaginary part. The results are refined if we consider the Hermitian matrix polynomial to be a perturbation of a ?-even polynomials; however, this refinement requires additional assumptions on the matrix coefficients. 相似文献
12.
Nataliya Protsakh 《Mathematical Methods in the Applied Sciences》2021,44(1):617-633
In this paper, we consider the inverse problem for second‐order semilinear ultraparabolic equation. The equation has unknown function of time variable in its minor coefficient and two unknown functions of time and spacial variables in its right‐hand side. Initial, boundary, and integral type overdetermination conditions are posed. By using the properties of the solutions of the corresponding initial‐boundary value problem and the method of successive approximations, the sufficient conditions of the existence, and the uniqueness of the solution for the inverse problem are obtained on some time interval that depends on the coefficients of the equation. 相似文献
13.
We obtain the solution of the stationary heat-conduction problem for a space with a cubic cavity under the assumption that
the coefficient of thermal conductivity depends on the temperature. The surfaces of the cavity are subject to heat flux. By
using the Kirchhoff variable and the method of continuation of functions we reduce the problem to a linear differential equation
with singular coefficients on the right-hand side. We conduct a numerical study of the temperature distribution as a function
of the spatial coordinate and the Kirpichev criterion that characterizes the thermal flux density.
Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 94–100. 相似文献
14.
PERUMPANANI ABBEY J.; SHERRATT JONATHAN A.; MAINI PHILIP K. 《IMA Journal of Applied Mathematics》1995,55(1):19-33
The authors study the effect of advection on reaction-diffusionpatterns. It is shown that the addition of advection to a two-variablereactiondiffusion system with periodic boundary conditionsresults in the appearance of a phase difference between thepatterns of the two variables which depends on the differencebetween the advection coefficients. The spatial patterns movelike a travelling wave with a fixed velocity which depends onthe sum of the advection coefficients. By a suitable choiceof advection coefficients, the solution can be made stationaryin time. In the presence of advection a continuous change inthe diffusion coefficients can result in two Turing-type bifurcationsas the diffusion ratio is varied, and such a bifurcation canoccur even when the inhibitor species does not diffuse. It isalso shown that the initial mode of bifurcation for a givendomain size depends on both the advection and diffusion coefficients.These phenomena are demonstrated in the numerical solution ofa particular reactiondiffusion system, and finally apossible application of the results to pattern formation inDrosophila larvae is discussed. 相似文献
15.
Statistical Inference for Stochastic Processes - In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on $$\mu $$ and volatility coefficient depends on... 相似文献
16.
In this paper we study the limiting values of the lift and drag coefficients of profiles in the Helmholtz-Kirchhoff (infinite cavity) flow. The coefficients are based on the wetted arc length of profile surfaces. Namely, for a given value of the lift coefficient we find minimum and maximum values of the drag coefficient. Thereby we determine maximum and minimum values of the lift-to-drag ratios. 相似文献
17.
Domain decomposition for multiscale PDEs 总被引:3,自引:1,他引:2
We consider additive Schwarz domain decomposition preconditioners for piecewise linear finite element approximations of elliptic
PDEs with highly variable coefficients. In contrast to standard analyses, we do not assume that the coefficients can be resolved
by a coarse mesh. This situation arises often in practice, for example in the computation of flows in heterogeneous porous
media, in both the deterministic and (Monte–Carlo simulated) stochastic cases. We consider preconditioners which combine local
solves on general overlapping subdomains together with a global solve on a general coarse space of functions on a coarse grid.
We perform a new analysis of the preconditioned matrix, which shows rather explicitly how its condition number depends on
the variable coefficient in the PDE as well as on the coarse mesh and overlap parameters. The classical estimates for this
preconditioner with linear coarsening guarantee good conditioning only when the coefficient varies mildly inside the coarse
grid elements. By contrast, our new results show that, with a good choice of subdomains and coarse space basis functions,
the preconditioner can still be robust even for large coefficient variation inside domains, when the classical method fails
to be robust. In particular our estimates prove very precisely the previously made empirical observation that the use of low-energy
coarse spaces can lead to robust preconditioners. We go on to consider coarse spaces constructed from multiscale finite elements
and prove that preconditioners using this type of coarsening lead to robust preconditioners for a variety of binary (i.e.,
two-scale) media model problems. Moreover numerical experiments show that the new preconditioner has greatly improved performance
over standard preconditioners even in the random coefficient case. We show also how the analysis extends in a straightforward
way to multiplicative versions of the Schwarz method.
We would like to thank Bill McLean for very useful discussions concerning this work. We would also like to thank Maksymilian
Dryja for helping us to improve the result in Theorem 4.3. 相似文献
18.
Ronald C. King 《Journal of Combinatorial Theory, Series A》2009,116(2):314-333
The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients. 相似文献
19.
该文利用数值方法模拟了封闭腔体的排液流动,获取了排液孔的流量系数.通过量纲分析法研究了小孔流量系数的主要影响因素,拟合了计算小孔流量系数的经验公式.结果表明:当水头高度小于200 mm时,小孔流量系数随水头高度的增加而减小;当水头高度大于200 mm时,小孔流量系数稳定在0.61附近.不同厚径比的小孔流量系数表现为两种不同的形式:小厚径比的小孔呈现薄孔流动特性,流量系数为0.6左右;大厚径比的小孔呈现厚孔流动特性,流量系数为0.8左右. 相似文献
20.
G.L. Silver 《Applied mathematics and computation》2005,170(2):125-760
Four polynomial equations for interpolating the nine-point cube are compared. All of the equations estimate first-, second- and third-order coefficients. Fidelity to monotonic test surfaces, as measured by sums-of-squares of deviations, depends on the distribution of the center point datum among the coefficients. Linear-term coefficients rendered by the equations are often more accurate than the like coefficients rendered by main-effects formulas. 相似文献