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2011 Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition
Jukka Kemppainen
Abstr. Appl. Anal. 2011: 1-11 (2011). DOI: 10.1155/2011/321903

Abstract

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.

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Jukka Kemppainen. "Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition." Abstr. Appl. Anal. 2011 1 - 11, 2011. https://doi.org/10.1155/2011/321903

Information

Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1218.35245
MathSciNet: MR2793790
Digital Object Identifier: 10.1155/2011/321903

Rights: Copyright © 2011 Hindawi

Vol.2011 • 2011
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