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math-ph2011★ 5 cited
The Role of Symmetry and Separation in Surface Evolution and Curve Shortening
Philip Broadbridge, Peter Vassiliou
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional se…
math-ph2010
Lie Symmetries and Exact Solutions of the Generalized Thin Film Equation
Roman Cherniha, Phil Broadbridge, Liliia Myroniuk
A symmetry group classification for fourth-order reaction-diffusion equations, allowing for both second-order and fourth-order diffusion terms, is carried out. The fourth order equ…