Mixed Stochastic Differential Equations: Existence and Uniqueness Result

In this paper we establish an existence and uniqueness result for solutions of multidimensional, time-dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter \(H>1/2\) and a multidimensional standard Brownian motion under a weaker condition than the Lipschitz one.     

热传导反问题中非线性热源的存在性

研究热传导方程在一类非局部时间的边界条件下线性热源的反演问题。文中应用Ｓｏｂｏｌｅｖ紧性方法证明了热源在Ｈｏｅｌｄｅｒ空间中的（关于时间的）局部存在性。     

An Inverse Heat Conduction Problem

In this paper, an inverse heat conduction problem will be considered. By reducing this inverse problem and using an overspecified condition, it is shown that the solution to the problem exists, and this solution is unique.AMS Subject Classification (2000): 45D05, 34A55     

Existence and Uniqueness to a Dynamic Bilateral Frictional Contact Problem in Viscoelasticity

In this paper we examine an evolution problem which describes the dynamic bilateral contact of a viscoelastic body and a foundation. The contact is modeled by a friction multivalued subdifferential boundary condition which incorporates the Coulomb law of friction, the SJK model and the orthotropic friction law. The main result concerns the existence and uniqueness of weak solutions to the hyperbolic variational inequality when the friction coefficient is sufficiently small. The proof is based on a surjectivity result for multivalued operators and a fixed point argument. Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.     

声学反问题的整体唯一性

It is proved that a sound-soft scatterer in R^N （N = 2, 3） is uniquely determined by a finite number of acoustic far-field measurements. The admissible scatterer possibly consists of finitely many solid obstacles and subsets of （N - 1）- dimensional hyperplanes.     

Existence and Uniqueness of the Cauchy Problem for a Generalized Navier-Stokes Equations

We consider the Cauchy problem for a generalized Navier-Stokes equations with hyperdissipation, with the initial data in L^p_σ. We follow the theme of [1] but with more complicated analysis on the symbol and obtain the existence and uniqueness results.     

z一致连续的倒向随机微分方程解的一个存在唯一性结果

建立了关于一维倒向随机微分方程(简写为BSDE)的一个存在唯一性结果,其中BSDE的生成元g关于y满足Constantin条件,关于z是一致连续的.这改进了一些已知结果.     

On the Uniqueness and Existence Problem for a Multidimensional Reacting and Convection System

The paper is concerned with the uniqueness and existence problemfor a multidimensional reacting and convection system with thevanishing viscosity method. The uniqueness theorem is obtainedfrom the stability with respect to the initial data. To solvethe existence problem, the uniqueness and existence of solutionsto a viscous system are first proved, and then the L¹-modulusof continuity of solutions independent of the small viscosityis obtained.     

关于变动边界的热传导问题

In this paper, a kind of heat conduction problem subject to a moving boundary condition is studied, in which its equation has form of quasilinear parabolic e-quation with vaviable coefficients, under some assumptions, we have defined and provided existence of solution of this problem in domain Ω by singular perturbation methods, where Ω denotes the domain:{σ₁(t)≤x≤ σ₂(t), 0≤t相似文献   

Spectral Asymptotics for a Steady-State Heat Conduction Problem in a Perforated Domain

In this paper we study the eigenvalues and eigenfunctions of a boundary-value problem for an elliptic equation of second order with oscillatory coefficients in a periodically perforated domain when the boundary condition on the external boundary is of the first type and on the boundary of holes of the third type, for the case in which the linear dimension of the perforation period tends to zero. It is proved that these eigenvalues and eigenfunctions can be determined approximately via the eigenvalues and eigenfunctions of an essentially simpler Dirichlet problem for an elliptic equation with constant coefficients in a domain without holes. Estimates of errors in these approximations are given.     

反向热传导问题的一种新的正则化方法

讨论一个高维反向热传导问题,这是一个经典的严重不适定问题.关于这一问题我们给出一种新的正则化方法-改进的Tikhonov正则化方法,以恢复解对数据的连续依赖性.通过构造一个重要的不等式和提高先验光滑条件,获得正则解在0相似文献   

Numerical Approximation of First Eigenvalues for a Heat Conduction Problem

An eigenvalue problem for a differential operator connected with the heat conduction of a non-steady flow is considered. By using an iterative method for computing the eigenvalues of second kind Fredholm operators (see [1]-[11]) we derive approximation of first eigenvalues closer with respect to results appearing in preceding literature.     

一类渗透率反演问题解的存在性与唯一性

本根据Thierry Bourbie et al建立的测定致密岩心的渗透率的装置，交换相应的数学模型中的边界条件和附加条件位置，得到了相应正问题的解析解．尔后，运用偏微分方程反问题中的系数反演方法，构造出了反演渗透率的关系式，在此基础上，运用不动点定理讨论了解析反演解的存在性与唯一性．反演的结果表明：只要在L端持续测量t1时间间隔，则所给的附加条件可以唯一确定渗透率．     

Riemann-Stieltjes积分边值问题正解的存在唯一性

利用解的先验估计和极值原理,研究了一类具有Riemann-Stieltjes积分边值问题正解的存在唯一性．     

一类带扰动项的拟线性抛物型方程解的存在性

主要利用算子的性质证明了一类带扰动项的拟线性方程的L~2(Ω)初值和狄立克莱边值问题解的存在性和唯一性.     

一类不定常热耦合Stokes问题:存在性,唯一性和解的爆破

研究了一类具有与时间相关的黏性系数和黏性热的不定常不可压拟牛顿流问题,即一类不定常热耦合Stokes问题.在一定条件下用Schauder不动点定理证明了弱解的存在性.通过建立弱解对初边值的估计式证明了解的唯一性.给出了有关解的爆破的结论.     

基于指数障碍期权的抛物方程的存在性和唯一性

考虑了一类基于指数障碍期权的拟线性抛物型方程.首先在b(t,x)=c(t,x)=0情形下运用标准的Schauder理论证明了该抛物型方程问题存在一个属于Cα,1+α/2的唯一解.其次,运用变换的方法将该结论推广到了一般方程.     

一类球型区域上变系数反向热传导问题

考虑了一类球型区域上变系数反向热传导问题.这个问题是不适定的,即问题的解(若存在)并不连续依赖于测量数据.构造了投影迭代正则化方法,得到了该反问题的正则近似解,同时给出了在先验和后验参数选取规则下精确解与正则近似解之间的收敛性误差估计.最后,通过数值结果验证了该方法的有效性.