Fractional partial differential equations with boundary conditions
Artikel i vetenskaplig tidskrift, 2018

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 C 0 (Ω) and L 1 (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.

Författare

Boris Baeumer

University of Otago

Mihaly Kovacs

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Harish Sankaranarayanan

Michigan State University

Journal of Differential Equations

0022-0396 (ISSN) 1090-2732 (eISSN)

Vol. 264 2 1377-1410

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1016/j.jde.2017.09.040