Boundary Integral Solution of the Time-Fractional Diffusion Equation |
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Authors: | J Kemppainen K Ruotsalainen |
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Institution: | (1) Mathematics Division, University of Oulu, P.O. Box 4500, FI-90014 Oulu, Finland |
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Abstract: | Here we consider initial boundary value problem for the time–fractional diffusion equation by using the single layer potential
representation for the solution. We derive the equivalent boundary integral equation. We will show that the single layer potential
admits the usual jump relations and discuss the mapping properties of the single layer operator in the anisotropic Sobolev
spaces. Our main theorem is that the single layer operator is coercive in an anisotropic Sobolev space. Based on the coercivity
and continuity of the single layer operator we finally show the bijectivity of the operator in a certain range of anisotropic
Sobolev spaces.
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 31A10 Secondary 26A33 |
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