Abstract
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.
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Chamard, J., Otta, J. & Lloyd, D.J.B. Computation of Minimum Energy Paths for Quasi-Linear Problems. J Sci Comput 49, 180–194 (2011). https://doi.org/10.1007/s10915-011-9462-x
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DOI: https://doi.org/10.1007/s10915-011-9462-x