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A Fokker-Planck type approximation of parabolic PDEs with oblique boundary data


Authors: Damon Alexander and Inwon Kim
Journal: Trans. Amer. Math. Soc. 368 (2016), 5753-5781
MSC (2010): Primary 35K55
Published electronically: August 20, 2015
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Abstract: We consider solutions of quasi-linear parabolic PDEs with zero oblique boundary data in a bounded domain. Our main result states that the solutions can be approximated by solutions of a Fokker-Planck type PDE in the whole space with a penalizing drift term which also converges to zero outside the original domain. The convergence is locally uniform, and optimal error estimates are obtained.


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Additional Information

Damon Alexander
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555
Email: d.alexander6@gmail.com

Inwon Kim
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095-1555
Email: ikim@math.ucla.edu

DOI: https://doi.org/10.1090/tran/6521
Received by editor(s): February 17, 2014
Received by editor(s) in revised form: May 2, 2014, and July 18, 2014
Published electronically: August 20, 2015
Article copyright: © Copyright 2015 American Mathematical Society