Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces
Joint Authors
Avalishvili, Gia
Avalishvili, Mariam
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-06-12
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Nonclassical problem for ultraparabolic equation with nonlocal initial condition with respect to one time variable is studied in abstract Hilbert spaces.
We define the space of square integrable vector-functions with values in Hilbert spaces corresponding to the variational formulation of the nonlocal problem for ultraparabolic equation and prove trace theorem, which allows one to interpret initial conditions of the nonlocal problem.
We obtain suitable a priori estimates and prove the existence and uniqueness of solution of the nonclassical problem and continuous dependence upon the data of the solution to the nonlocal problem.
We consider an application of the obtained abstract results to nonlocal problem for ultraparabolic partial differential equation with second-order elliptic operator and obtain well-posedness result in Sobolev spaces.
American Psychological Association (APA)
Avalishvili, Gia& Avalishvili, Mariam. 2016. Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1108621
Modern Language Association (MLA)
Avalishvili, Gia& Avalishvili, Mariam. Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces. Journal of Function Spaces No. 2016 (2016), pp.1-15.
https://search.emarefa.net/detail/BIM-1108621
American Medical Association (AMA)
Avalishvili, Gia& Avalishvili, Mariam. Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1108621
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108621