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On a backward problem for multidimensional Ginzburg-Landau equation with random data
Journal article   Peer reviewed

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

Mokhtar Kirane, Erkan Nane and Nguyen Huy Tuan
Inverse problems, Vol.34(1), p.15008
01/01/2018
DOI: https://doi.org/10.1088/1361-6420/aa9c2a

Abstract

backward problem ill-posed problem regularization
In this paper, we consider a backward in time problem for the Ginzburg-Landau equation in a 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. We prove an upper bound on the rate of convergence of the mean integrated squared error in L2 and H1 norms.

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