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Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition
Author
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-05-08
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition on a bounded domain with Lyapunov boundary is proved in the space of continuous functions up to boundary.
Since a Green matrix of the problem is known, we may seek the solution as the linear combination of the single-layer potential, the volume potential, and the Poisson integral.
Then the original problem may be reduced to a Volterra integral equation of the second kind associated with a compact operator.
Classical analysis may be employed to show that the corresponding integral equation has a unique solution if the boundary data is continuous, the initial data is continuously differentiable, and the source term is Hölder continuous in the spatial variable.
This in turn proves that the original problem has a unique solution.
American Psychological Association (APA)
Kemppainen, Jukka. 2011. Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-11.
https://search.emarefa.net/detail/BIM-463404
Modern Language Association (MLA)
Kemppainen, Jukka. Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition. Abstract and Applied Analysis No. 2011 (2011), pp.1-11.
https://search.emarefa.net/detail/BIM-463404
American Medical Association (AMA)
Kemppainen, Jukka. Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-11.
https://search.emarefa.net/detail/BIM-463404
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463404