Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and.-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.

### Group analysis and heir-equations of a mathematical model for thin liquid films

#### Abstract

Lie group analysis is applied to a mathematical model for thin liquid films, namely a nonlinear fourth order partial differential equation in two independent variables. A three-dimensional Lie symmetry algebra is found and reductions to fourth order ordinary differential equations are obtained by using its one-dimensional subalgebras. Two of these ordinary differential equations are studied by the reduction method and by the Jacobi last multiplier method, and found to be linearizable. Furthermore, the G-equation and.-equation, namely two of the heir-equations obtained by iterating the nonclassical symmetries method, are constructed and reductions to different ordinary differential equations are acquired by using two-dimensional and three-dimensional subalgebras, respectively.
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2009
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/3213765`
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