A Fokker-Planck type approximation of parabolic PDEs with oblique boundary data
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- by Damon Alexander and Inwon Kim PDF
- Trans. Amer. Math. Soc. 368 (2016), 5753-5781 Request permission
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.References
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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
- MR Author ID: 684869
- Email: ikim@math.ucla.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 5753-5781
- MSC (2010): Primary 35K55
- DOI: https://doi.org/10.1090/tran/6521
- MathSciNet review: 3458398