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

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.

Authors
Kirane M. 1, 2, 3 , Nane E.4 , Tuan N.H.5
Publisher
Institute of Physics Publishing
Number of issue
1
Language
English
Status
Published
Number
015008
Volume
34
Year
2018
Organizations
  • 1 LaSIE, Facult des Sciences EtTechnologies, Universi de la Rochelle, Avenue M. Crpeau, La Rochelle, Cedex, 17042, France
  • 2 Nonlinear Analysis and Applied Mathematics, (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
  • 3 RUDN University, 6 Miklukho-MaklaySt, Moscow, 117198, Russian Federation
  • 4 Department of Mathematics and Statistics, Auburn University, Auburn, AL, United States
  • 5 Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
Keywords
backward problem; ill-posed problem; regularization
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/7343/