TY - JOUR
T1 - Solution for 4th-order nonlinear axisymmetric surface diffusion by inverse method
AU - Gallage, Dilruk
AU - Triadis, Dimetre
AU - Broadbridge, Philip
AU - Cesana, Pierluigi
N1 - Funding Information:
D. Gallage gratefully acknowledges the support of a La Trobe University postgraduate scholarship, while on study leave from the University of Colombo. P. Cesana is supported by JSPS grants 16K21213 and 19H05131 , holds an honorary appointment at La Trobe University and is a member of GNAMPA. This research is an activity of Kyushu University’s Institute of Mathematics for Industry (IMI) — Australia Branch, which is managed with generous support from Kyushu University, La Trobe University, and the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
Funding Information:
D. Gallage gratefully acknowledges the support of a La Trobe University postgraduate scholarship, while on study leave from the University of Colombo. P. Cesana is supported by JSPS grants 16K21213 and 19H05131, holds an honorary appointment at La Trobe University and is a member of GNAMPA. This research is an activity of Kyushu University's Institute of Mathematics for Industry (IMI) — Australia Branch, which is managed with generous support from Kyushu University, La Trobe University, and the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/4
Y1 - 2020/4
N2 - We present a method for constructing similarity solutions of a fourth-order nonlinear partial differential equation for axisymmetric surface diffusion by extending an inverse method previously used for the second-order one-dimensional nonlinear diffusion equation. After imposing a solution profile, both a feasible surface tension, and a compatible mobility function are deduced simultaneously. Although the profile is not one-to-one, an optimization algorithm is implemented to construct a mobility function that is a function of surface orientation, with no practical difference in mobility between different arms of the many-to-one profile. It is shown that the solution of the linear model well approximates the solution of the nonlinear model, in which the surface tension and mobility are close to constant for a wide range of surface angles, even when nonlinear geometric terms are included.
AB - We present a method for constructing similarity solutions of a fourth-order nonlinear partial differential equation for axisymmetric surface diffusion by extending an inverse method previously used for the second-order one-dimensional nonlinear diffusion equation. After imposing a solution profile, both a feasible surface tension, and a compatible mobility function are deduced simultaneously. Although the profile is not one-to-one, an optimization algorithm is implemented to construct a mobility function that is a function of surface orientation, with no practical difference in mobility between different arms of the many-to-one profile. It is shown that the solution of the linear model well approximates the solution of the nonlinear model, in which the surface tension and mobility are close to constant for a wide range of surface angles, even when nonlinear geometric terms are included.
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U2 - 10.1016/j.physd.2019.132288
DO - 10.1016/j.physd.2019.132288
M3 - Article
AN - SCOPUS:85079383580
SN - 0167-2789
VL - 405
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
M1 - 132288
ER -