Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/78713
Title: Boundary problems for the fractional and tempered fractional operators
Authors: Deng, WH
Li, BY 
Tian, WY
Zhang, PW
Keywords: Levy flight
Tempered Levy flight
Well-posedness
Generalized boundary conditions
Issue Date: 2018
Publisher: Society for Industrial and Applied Mathematics
Source: Multiscale modeling & simulation, 2018, v. 16, no. 1, p. 125-149 How to cite?
Journal: Multiscale modeling & simulation 
Abstract: To characterize the Brownian motion in a bounded domain Omega, it is well known that the boundary conditions of the classical diffusion equation just rely on the given information of the solution along the boundary of a domain; in contrast, for the Levy flights or tempered Levy flights in a bounded domain, the boundary conditions involve the information of a solution in the complementary set of Omega, i.e., R-n\Omega, with the potential reason that paths of the corresponding stochastic process are discontinuous. Guided by probability intuitions and the stochastic perspectives of anomalous diffusion, we show the reasonable ways, ensuring the clear physical meaning and well-posedness of the partial differential equations (PDEs), of specifying "boundary" conditions for space fractional PDEs modeling the anomalous diffusion. Some properties of the operators are discussed, and the well-posednesses of the PDEs with generalized boundary conditions are proved.
URI: http://hdl.handle.net/10397/78713
ISSN: 1540-3459
EISSN: 1540-3467
DOI: 10.1137/17M1116222
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