The generalized convective Cahn–Hilliard equation: Symmetry classification, power series solutions and dynamical behavior

2019 ◽  
Vol 31 (02) ◽  
pp. 2050024
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma ◽  
Li-Sheng Zhang

We first perform a complete Lie symmetry classification of the generalized convective Cahn–Hilliard equation. Then using the obtained symmetries, we mainly study the convective Cahn–Hilliard equation, of which a new power series solution is constructed. In particular for the crystal surface growth processes, the truncated series solution shows that the surface structures include peaks and valleys, and can exhibit different evolution trends with the driving force varying from compressive force to tensile force. Moreover, there exist several critical points for the driving force, where the surface configurations take the jump changes and show different features on the both sides of such critical points. According to the effects of driving forces, we analyze the dynamical features of crystal growth.

2017 ◽  
Vol 72 (3) ◽  
pp. 261-267 ◽  
Author(s):  
Zhi-Yong Zhang ◽  
Kai-Hua Ma

AbstractWe perform a complete Lie point symmetry classification of the generalised foam-drainage equation and then construct an optimal system of one-dimensional subalgebra of the admitted symmetry operators and use them to reduce the equations under study. A power series solution of the reduced equation is constructed. Moreover, we find all multipliers of the equations and apply them to construct conservation laws.


2021 ◽  
Vol 25 (8) ◽  
pp. 6075-6082
Author(s):  
Hemanta Mandal ◽  
B. Bira ◽  
D. Zeidan

1970 ◽  
Vol 48 (5) ◽  
pp. 752-763 ◽  
Author(s):  
A. D. Pelton

A general analytical power-series solution of the Gibbs–Duhem equation in multicomponent systems of any number of components has been developed. The simplicity and usefulness of the solution is made possible through the choice of a special set of composition variables.


Author(s):  
Hiroto Inoue

A matrix-valued extension of the Bratu equation is defined. For its initial value problem, the exponential matrix solution and power series solution are provided.


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