A FOKKER-PLANCK TYPE APPROXIMATION OF PARABOLIC PDES WITH OBLIQUE BOUNDARY DATA

作者:Alexander Damon*; Kim Inwon*
来源:Transactions of the American Mathematical Society, 2016, 368(8): 5753-5781.
DOI:10.1090/tran/6521

摘要

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.

  • 出版日期2016-8