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

Abstract

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.

15 pages; submitted for publication. arXiv admin note: text overlap with arXiv:1701.08459

References in corpus (1)

• Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise