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Archive for Rational Mechanics and Analysis

, Volume 229, Issue 2, pp 601–625 | Cite as

Three-Scale Singular Limits of Evolutionary PDEs

  • Bin Cheng
  • Qiangchang Ju
  • Steve SchochetEmail author
Open Access
Article

Abstract

Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly bounded for a fixed time as the two parameters tend to zero at different rates. A simple example shows the necessity of those conditions in order for uniform bounds to hold. Under further conditions the solutions of the original system tend to solutions of a limit equation as the parameters tend to zero.

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SurreyGuildfordUK
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingChina
  3. 3.School of Mathematical SciencesTel-Aviv UniversityTel AvivIsrael

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