arXiv 1702.030242017-02-10math.APmath-phmath.MPmath.PRmath.SP

On a backward problem for multidimensional Ginzburg-Landau equation with random data

Mokhtar Kirane, Erkan Nane, Nguyen Huy Tuan

备注：: 15 pages; submitted for publication. arXiv admin note: text overlap with arXiv:1701.08459
DOI：: 10.1088/1361-6420/aa9c2a

英文摘要：

In this paper, we consider a backward in time problem for Ginzburg-Landau equation in multidimensional domain associated with some random data. The problem is ill-posed in the sense of Hadamard. To regularize the instable solution, we develop a new regularized method combined with statistical approach to solve this problem. We prove a upper bound, on the rate of convergence of the mean integrated squared error in $L^2 $ norm and $H^1$ norm.

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