Journal of Scientific Computing

, Volume 49, Issue 2, pp 180–194 | Cite as

Computation of Minimum Energy Paths for Quasi-Linear Problems

  • Jeremy Chamard
  • Josef Otta
  • David J. B. Lloyd


We investigate minimum energy paths of the quasi-linear problem with the p-Laplacian operator and a double-well potential. We adapt the String method of E, Ren, and Vanden-Eijnden (J. Chem. Phys. 126, 2007) to locate saddle-type solutions. In one-dimension, the String method is shown to find a minimum energy path that can align along one-dimensional “ridges” of saddle-continua. We then apply the same method to locate saddle solutions and transition paths of the two-dimensional quasi-linear problem. The method developed is applicable to a general class of quasi-linear PDEs.


p-Laplacian String method Mountain pass algorithm 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Jeremy Chamard
    • 1
  • Josef Otta
    • 2
  • David J. B. Lloyd
    • 1
  1. 1.Department of MathematicsUniversity of SurreyGuildfordUK
  2. 2.Department of MathematicsUniversity of West BohemiaPlzeňCzech Republic

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