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On singular perturbation in non well posed problems

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Summary

Let Lεu and L 0 v be the elliptic and “backward” heat operators defined by(1.1) and(1.2), respectively. The following question is considered for a pair of “non-well posed” initial-boundary value problems for Lε and L 0 : if u and v are the respective solutions, under what restrictions on the classes of admissible solutions and in what sense, if any, does u converge to v as ɛ →0?

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Additional information

This research was supported in part by the National Science Foundation Grant No. GP 5882 with Cornell University.

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Payne, L.E., Sather, D. On singular perturbation in non well posed problems. Annali di Matematica 75, 219–230 (1967). https://doi.org/10.1007/BF02416803

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Keywords

  • Singular Perturbation
  • Admissible Solution
  • Heat Operator
  • Respective Solution