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COERCIVENESS INEQUALITIES FOR ABSTRACT PARABOLIC EQUATIONS, 157
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Springer Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-012-0156-0
- Publisher site
- See Article on Publisher Site
Abstract
We prove the global strong solvability of a quasilinear initial-boundary value problem with fractional time derivative of order less than one. Such problems arise in mathematical physics in the context of anomalous diffusion and the modeling of dynamic processes in materials with memory. The proof relies heavily on a regularity result on the interior Hölder continuity of weak solutions to time fractional diffusion equations, which has been proved recently by the author. We further establish an L 2 decay estimate for the special case with vanishing external source term and homogeneous Dirichlet boundary condition.
Journal
Journal of Evolution Equations – Springer Journals
Published: Dec 1, 2012