Regularity of solutions to a time-fractional diffusion equation

William McLean

Abstract


We prove estimates for the partial derivatives of the solution to a time-fractional diffusion equation posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is typically less regular than in the familiar case of classical diffusion.

doi:10.1017/S1446181111000617

Keywords


fractional derivative; Laplace transform; Sobolev space; singular behaviour



DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3593



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.