Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes

D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Richard

doi:10.1515/cmam-2017-0029

Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes

Journal Article · Thu Aug 31 00:00:00 EDT 2017 · Computational Methods in Applied Mathematics

DOI:https://doi.org/10.1515/cmam-2017-0029· OSTI ID:1469622

D’Elia, Marta ^[1]; ^[2]; Gunzburger, Max ^[3]; ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
Columbia Univ., New York, NY (United States). Dept. of Applied Physics and Applied Mathematics. Fu Foundation School of Engineering and Applied Sciences
Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing

In this paper, a nonlocal convection-diffusion model is introduced for the master equation of Markov jump processes in bounded domains. With minimal assumptions on the model parameters, the nonlocal steady and unsteady state master equations are shown to be well-posed in a weak sense. Finally, then the nonlocal operator is shown to be the generator of finite-range nonsymmetric jump processes and, when certain conditions on the model parameters hold, the generators of finite and infinite activity Lévy and Lévy-type jump processes are shown to be special instances of the nonlocal operator.

View Accepted Manuscript (DOE)

Research Organization:: Columbia Univ., New York, NY (United States); Florida State Univ., Tallahassee, FL (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: Air Force Office of Scientific Research (AFOSR) (United States); Army Research Office (ARO) (United States); Defense Advanced Research Projects Agency (DARPA) (United States); National Science Foundation (NSF) (United States); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: NA0003525; SC0009324

OSTI ID:: 1469622

Report Number(s):: SAND2018--9655J; 667563

Journal Information:: Computational Methods in Applied Mathematics, Journal Name: Computational Methods in Applied Mathematics Journal Issue: 4 Vol. 17; ISSN 1609-4840

Publisher:: de GruyterCopyright Statement

Country of Publication:: United States

Language:: English

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Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes

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