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991.
考虑了一类二维非线性时间分数阶扩散方程,并从最终位置获取的测量数据来反演物质在u(0, y, t)处的物理信息。这个问题是严重不适定的,即问题的解并不连续依赖于测量数据,因此提出了变分型正则化方法来稳定求解该问题。给出了精确解与正则近似解之间的误差估计,数值算例验证了该方法的有效性。 相似文献
992.
Manal Aoudj 《Journal of Nonlinear Modeling and Analysis》2022,4(1):1-17
We consider a nonlinear inverse problem for an elliptic partial differential equation known as the Calder{\''o}n problem or the inverse conductivity problem. Based on several results, we briefly summarize them to motivate this research field. We give a general view of the problem by reviewing the available results for $C^2$ conductivities. After reducing the original problem to the inverse problem for a Schr\"odinger equation, we apply complex geometrical optics solutions to show its uniqueness. After extending the ideas of the uniqueness proof result, we establish a stable dependence between the conductivity and the boundary measurements. By using the Carleman estimate, we discuss the partial data problem, which deals with measurements that are taken only in a part of the boundary. 相似文献
993.
In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-E′mery Ricci tensor bounded below: One is u_t=Δ_fu + aulogu+bu with a, b two real constants, and another is u_t = Δ_fu+λu~α with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f. 相似文献
994.
Michael V. Klibanov Vladimir G. Kamburg 《Mathematical Methods in the Applied Sciences》2016,39(4):930-940
A coefficient inverse problem for a parabolic equation is considered. Using a Carleman weight function, a globally strictly convex cost functional is constructed for this problem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
995.
Luan Thach Hoang 《Journal of Differential Equations》2008,245(9):2585-2594
We show that ‖Au+Δu‖L2(Ωε)?C(ε‖∇u‖L2(Ωε)+‖u‖L2(Ωε)), where Ωε is a thin domain in R3 of depth ε, the vector field u belongs to the domain of A, which is the Stokes operator for divergence-free vector fields on Ωε satisfying the Navier boundary condition. 相似文献
996.
In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes
Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE
and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods
such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each
observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations
according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated
situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of
many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor.
The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm
the advantage of WVE.
This work was supported by National Natural Science Foundation of China (Grant No. 10771015) 相似文献
997.
998.
For the isotropic stationary Lamé system with variable coefficients equipped with the Dirichlet or surface stress boundary condition, we obtain a Carleman estimate such that (i) the right hand side is estimated in a weighted L 2-space and (ii) the estimate includes nonhomogeneous surface displacement or surface stress. Using this estimate we establish the conditional stability in Sobolev's norm of the displacement by means of measurements in an arbitrary subdomain or measurements of surface displacement and stress on an arbitrary subboundary. Finally by the Carleman estimate, we prove the uniqueness and conditional stability for an inverse problem of determining a source term by a single interior measurement. 相似文献
999.
In this paper, error estimates for the finite point method are presented in Sobolev spaces in multiple dimensions when nodes and shape functions satisfy certain conditions. From the error analysis of the finite point method, the error bound of the numerical solution is directly related to the radii of the weight functions and the condition number of the coefficient matrix. 相似文献
1000.