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91.
This work studies the inverse problem of reconstructing an initial value function in the degenerate parabolic equation using the final measurement data. Problems of this type have important applications in the field of financial engineering. Being different from other inverse backward parabolic problems, the mathematical model in our article may be allowed to degenerate at some part of boundaries, which may lead to the corresponding boundary conditions missing. The conditional stability of the solution is obtained using the logarithmic convexity method. A finite difference scheme is constructed to solve the direct problem and the corresponding stability and convergence are proved. The Landweber iteration algorithm is applied to the inverse problem and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown initial value is recovered very well.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1900–1923, 2017 相似文献
92.
We give an existence result of the obstacle parabolic equations(b(x,u))/(t)-div(a(x,t,u,▽u))+div(φ(x,t,u))=f in Q_T,where b(x,u) is bounded function of u,the term-div(a(x,t,u,▽u)) is a Leray-Lions type operator and the function φ is a nonlinear lower order and satisfy only the growth condition.The second term f belongs to L~1(Q_T).The proof of an existence solution is based on the penalization methods. 相似文献
93.
Krzysztof A. Topolski 《Czechoslovak Mathematical Journal》2008,58(4):927-947
We consider the initial-boundary value problem for first order differential-functional equations. We present the ‘vanishing
viscosity’ method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument
and differential-integral equations.
Supported by KBN grant 2 PO3A, 01811. 相似文献
94.
In this paper we consider the 2-dimensional flow of a Stokesian fluid in a Hele-Shaw cell. The motion of the flow is modelled
by a modified Darcy’s law. The existence of local solutions has been proved by the authors in a recent work, cf. [4]. The
purpose of this paper is to identify the steady states of this flow and to study their stability.
The equilibria will be identified as solutions of elliptic free boundary problems. It is shown that if the pressure on the
bottom is constant then the corresponding steady state is asymptotically stable.
相似文献
95.
C. Durot 《Mathematical Methods of Statistics》2008,17(4):327-341
In this paper we study the nonparametric least squares estimator of a regression function in a random design setting under
the constraint that this function is monotone, say, nonincreasing. The errors are not assumed conditionally i.i.d. given the
observation points. In particular, this includes the case of conditional heteroscedasticity and the case of the current status
model. The -error is shown to be of order n
−p/3 and asymptotically Gaussian with explicit asymptotic mean and variance.
相似文献
96.
Email: gugat{at}am.uni-erlangen.de
Received on April 30, 2006; We consider a finite string that is fixed at one end and subjectto a feedback control at the other end which is allowed to move.We show that the behaviour is similar to the situation whereboth ends are fixed: As long as the movement is not too fast,the energy decays exponentially and for a certain parameterin the feedback law it vanishes in finite time. We considermovements of the boundary that are continuously differentiablewith a derivative whose absolute value is smaller than the wavespeed. We solve a problem of worst-case optimal feedback control,where the parameter in the feedback law is chosen such thatthe worst-case Lp-norm of the space derivative at the fixedend of the string is minimized (p [1, )). We consider the worstcase both with respect to the initial conditions and with respectto the boundary movement. It turns out that the parameter forwhich the energy vanishes in finite time is optimal in thissense for all p. 相似文献
97.
对四维抛物型方程构造了一个高精度显格式,格式的稳定性条件为r=Δt/Δx2=△t/Δy2=△t/△z2=Δt/Δw2<1/2,截断误差阶达到O(Δt2 Δx4),通过数值实验,表明本文理论分析的正确性和文中格式较同类格式的优越性. 相似文献
98.
L.E. Payne 《Journal of Mathematical Analysis and Applications》2008,338(1):438-447
A first order differential inequality technique is used on suitably defined auxiliary functions to determine lower bounds for blow-up time in initial-boundary value problems for parabolic equations of the form
ut=div(ρ(u)gradu)+f(u) 相似文献
99.
半线性抛物方程各向异性最低阶R-T混合元超收敛分析 总被引:2,自引:2,他引:2
利用各向异性判别定理验证了最低阶数R-T混合元具有各向异性特征.利用积分恒等式技巧,得到了R-T元对半线性抛物方程的超逼近性质.通过构造新的插值后处理格式,导出了超收敛结果及后验误差估计. 相似文献
100.
This paper considers a semilinear elliptic equation on a n-dimensional complete noncompact Riemannian manifold,which is a generalization of the well known Yamabe equation.An existence result is proved. 相似文献