Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899104 | Journal of Differential Equations | 2018 | 34 Pages |
Abstract
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posedness of the associated Cauchy problems in C0(Ω) and L1(Ω). In order to do so we develop a new method of embedding finite state Markov processes into Feller processes on bounded domains and then show convergence of the respective Feller processes. This also gives a numerical approximation of the solution. The proof of well-posedness closes a gap in many numerical algorithm articles approximating solutions to fractional differential equations that use the Lax-Richtmyer Equivalence Theorem to prove convergence without checking well-posedness.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Boris Baeumer, Mihály Kovács, Harish Sankaranarayanan,