共查询到20条相似文献,搜索用时 15 毫秒
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On the exit law from saddle points 总被引:1,自引:0,他引:1
Martin V. Day 《Stochastic Processes and their Applications》1995,60(2):287-311
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A dynamical system perturbed by white noise in a neighborhood of an unstable fixed point is considered. We obtain the exit asymptotics in the limit of vanishing noise intensity. This is a refinement of a result by Kifer (1981). 相似文献
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The work presents a mathematical model describing the time fractional anomalous-diffusion process of a generalized Stefan problem which is a limit case of a shoreline problem. In this model, the governing equations include a fractional time derivative of order 0 < α ? 1 and variable latent heat. The approximate solution of the problem is obtained by homotopy perturbation method. The results thus obtained are compared graphically with the exact solutions. A brief sensitivity study is also performed. 相似文献
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The existence of a local classical solution to the Mullins-Sekerka problem and the convergence to the two-phase quasi-stationary
Stefan problem are proved when surface tension approaches zero. This convergence gives a proof of the existence of a local
classical solution of quasi-stationary Stefan problem. The methods work in all dimensions. 相似文献
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Nguyen Huy Tuan Nguyen Hoang Tuan Dumitru Baleanu Tran Ngoc Thach 《Mathematical Methods in the Applied Sciences》2020,43(3):1292-1312
In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L2 and Hτ norms is considered and illustrated by numerical example. 相似文献
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Classical verigin problem as a limit case of verigin problem with surface tension at free boundary 总被引:1,自引:0,他引:1
TAOYOUSHAN YIFAHUAI 《高校应用数学学报(英文版)》1996,11(3):307-322
In this psper we consider Verigin problem with surface tension st free 相似文献
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Georg Neuhaus 《Journal of multivariate analysis》1977,7(3):424-439
Sen (1974) established multidimensional functional limit theorems for generalized U-statistics for estimable parameters which are stationary of order zero (the nondegenerate case). Similar univariate and bivariate functional limit theorems are derived for U-statistics in the degenerate case. The latter are close connected with one- or two-sample Cramér-von Mises statistics. 相似文献
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Hikmet Koyunbakan Etibar S. Panakhov 《Journal of Mathematical Analysis and Applications》2007,326(2):1024-1030
The potential function q(x) in the regular and singular Sturm-Liouville problem can be uniquely determined from two spectra. Inverse problem for diffusion operator given at the finite interval eigenvalues, normal numbers also on two spectra are solved. Half-inverse spectral problem for a Sturm-Liouville operator consists in reconstruction of this operator by its spectrum and half of the potential. In this study, by using the Hochstadt and Lieberman's method we show that if q(x) is prescribed on , then only one spectrum is sufficient to determine q(x) on the interval for diffusion operator. 相似文献
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Identification of an inverse source problem for time‐fractional diffusion equation with random noise
Tran Ngoc Thach Tuan Nguyen Huy Pham Thi Minh Tam Mach Nguyet Minh Nguyen Huu Can 《Mathematical Methods in the Applied Sciences》2019,42(1):204-218
In this paper, we consider an inverse source problem for a time fractional diffusion equation. In general, this problem is ill posed, therefore we shall construct a regularized solution using the filter regularization method in the random noise case. We will provide appropriate conditions to guarantee the convergence of the approximate solution to the exact solution. Then, we provide examples of filters in order to obtain error estimates for their approximate solutions. Finally, we present a numerical example to show efficiency of the method. 相似文献
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We present a multiscale analysis for the exit measures from large balls in , of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment corresponding
to simple random walk. Our main assumption is an isotropy assumption on the law of the environment, introduced by Bricmont
and Kupiainen. Under this assumption, we prove that the exit measure of the random walk in a random environment from a large
ball, approaches the exit measure of a simple random walk from the same ball, in the sense that the variational distance between
smoothed versions of these measures converges to zero. We also prove the transience of the random walk in random environment.
The analysis is based on propagating estimates on the variational distance between the exit measure of the random walk in
random environment and that of simple random walk, in addition to estimates on the variational distance between smoothed versions
of these quantities.
Partially supported by NSF grant DMS-0503775. 相似文献
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Mohammad F. Al‐Jamal 《Mathematical Methods in the Applied Sciences》2017,40(7):2466-2474
In this paper, we are concerned with the backward problem of reconstructing the initial condition of a time‐fractional diffusion equation from interior measurements. We establish uniqueness results and provide stability analysis. Our method is based on the eigenfunction expansion of the forward solution and the Tikhonov regularization to tackle the ill‐posedness issue of the underlying inverse problem. Some numerical examples are included to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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In this paper, we study an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final measurement. First the given problem is transformed into an optimization problem by using optimal control framework and the existence of the minimizer for the control functional is established. Then we prove the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement. 相似文献
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Giambattista Giacomin Christophe Poquet Assaf Shapira 《Journal of Differential Equations》2018,264(2):1019-1049
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise – that is, we modulate the noise by a factor – and on a long time horizon. We prove explicit estimates on the proximity of the noisy trajectory and the limit cycle up to times , , and we show both that on the time scale the dephasing (i.e., the difference between noiseless and noisy system measured in a natural coordinate system that involves a phase) is close to a Brownian motion with constant drift, and that on longer time scales the dephasing dynamics is dominated by the drift. The natural choice of coordinates, that reduces the dynamics in a neighborhood of the cycle to a rotation, plays a central role and makes the connection with the applied science literature in which noisy limit cycle dynamics are often reduced to a diffusion model for the phase of the limit cycle. 相似文献