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Self-adjoint sub-classes of generalized thin film equations. (English) Zbl 1170.35439
Summary: We consider a class of fourth-order nonlinear partial differential equation containing several unspecified coefficient functions of the dependent variable which encapsulates various mathematical models used, e.g. for describing the dynamics of thin liquid films. We determine the subclasses of these equations which are self-adjoint. By using a general theorem on conservation laws proved by one of the authors (NHI) we find conservation laws for some of these partial differential equations without classical Lagrangians.
MSC:
35K25Higher order parabolic equations, general
76A20Thin fluid films (fluid mechanics)
58J70Invariance and symmetry properties
35K55Nonlinear parabolic equations