On a backward problem for multidimensional Ginzburg–Landau equation with random data. (15th December 2017) - Kirane, Mokhtar; Nane, Erkan; Tuan, Nguyen Huy
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.