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Group analysis of nonlinear fin equations. (English) Zbl 1160.35320
Summary: Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. These enable us to simplify the classification results and their further applications. The derived Lie symmetries are used to construct exact solutions of truly nonlinear equations for the class under consideration. Nonclassical symmetries of the fin equations are discussed. Adduced results complete and essentially generalize recent works on the subject [M. Pakdemirli and A. Z. Sahin, Appl. Math. Lett. 19, No. 4, 378–384 (2006; Zbl 1114.80003); Appl. Math. Lett. 19, No. 12, 1356–1360 (2006; Zbl 1143.35311)].

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
35K55 Nonlinear parabolic equations
74F05 Thermal effects in solid mechanics
58J70 Invariance and symmetry properties for PDEs on manifolds
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