On a backward problem for multidimensional Ginzburg–Landau equation with random data. (15th December 2017)

• Record Type: Journal Article
• Authors: Kirane, Mokhtar; Nane, Erkan; Tuan, Nguyen Huy
• Is Part Of: Inverse problems. Volume 34:Number 1(2018:Jan.)
• Publication Date: 2017-12-15
• Subjects: backward problem -- regularization -- ill-posed problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa9c2a
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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 L 2 and H 1 norms.