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
Journal
Inverse Problems
Publisher
Institute of Physics Publishing
Number of issue
1
Language
English
Status
Published
Link
External link
DOI
10.1088/1361-6420/AA9C2A
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
Cite
ГОСТ MLA RIS BibTex
Share

Other records

REDOX-DEPENDENT EXPRESSION OF GENES ENCODING NADPH OXIDASE 5 AND THE KEY ANTIOXIDANT ENZYMES DURING FORMATION OF DRUG RESISTANCE OF TUMOR CELLS TO CISPLATIN

Article
Kalinina E.V., Andreev Y.A., Petrova A.S., Lubova K.I., Shtil’ A.A., Chernov N.N., Novichkova M.D., Nurmuradov N.K.
Bulletin of Experimental Biology and Medicine. New York Consultants BureauSpringer / Автономная некоммерческая организация Издательство Российской академии медицинских наук. 2018.