Group classification of the equations of two-dimensional motions of a gas

Meleshko, Sergey V.

doi:10.1016/0021-8928(94)90138-4

Cited by 52 publications

(57 citation statements)

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“…Restrictions on transformations can be weakened in two directions. We admit that transformations of the variables t , x and u can depend on arbitrary elements (the prefix "generalized" [35]), and this dependence are not necessarily point and have to become point with respect to (t, x, u) after fixing values of arbitrary elements. The explicit form of the new arbitrary elements (f ,g,h,m) is determined via (t, x, u, f, g, h, m) in some nonfixed (possibly, nonlocal) way (the prefix "extended").…”

Section: Theorem 1 G ∼ Consists Of the Transformationsmentioning

confidence: 99%

“…To solve more group classification problems and to present results in an optimal way, different tools and notions (additional equivalence transformations, extended and generalized equivalence groups, conditional equivalence group, gauging of arbitrary elements by equivalence transformations, partition of a class to normalized subclasses etc.) were recently proposed [22,24,35,46,51]. Their usage had the critical value, in particular, for the complete group classifications of class (2), where n = 0, [51] and a class of variable coefficient diffusion-convection equations [24].…”

Section: Introductionmentioning

confidence: 99%

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Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

2008

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A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by families of point transformations. A class of variable coefficientis studied from the symmetry point of view in the framework of the approach proposed. The singular subclass of the equations with m = 2 is singled out. The group classifications of the entire class, the singular subclass and their images are performed with respect to both the corresponding (generalized extended) equivalence groups and all point transformations. The set of admissible transformations of the imaged class is exhaustively described in the general case m = 2. The procedure of classification of nonclassical symmetries, which involves mappings between classes of differential equations, is discussed. Wide families of new exact solutions are also constructed for equations from the classes under consideration by the classical method of Lie reductions and by generation of new solutions from known ones for other equations with point transformations of different kinds (such as additional equivalence transformations and mappings between classes of equations).

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Section: Theorem 1 G ∼ Consists Of the Transformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

2008

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“…The subclass of class (1) with D being a power function and h being a constant admits an extension of the generalized equivalence group. The prefix "generalized" means that transformations of the variables t, x and u can depend on arbitrary elements [8][9][10]. The associated generalized equivalence group G ∼ 3 is generated by transformations from G ∼ and the last of the above additional equivalence transformations, where ε is replaced by h.…”

Section: Group Classification and Related Problemsmentioning

confidence: 99%

Group analysis of nonlinear fin equations

Vaneeva

Johnpillai²,

Popovych

et al. 2008

Applied Mathematics Letters

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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 AA note on a symmetry analysis and exact solutions of a nonlinear fin equation, Appl.

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“…In Section 2 we seek the group of equivalence transformations for equation (1.1) by employing the approach suggested in [6,7]. In Section 3 we seek the specifications and the associated full symmetries groups for the equation expanding the kernel of full transformation groups.…”

Section: Introductionmentioning

confidence: 99%

Group classification of a class of semilinear pseudoparabolic equations

Panov¹

2013

Ufimskii Matematicheskii Zhurnal

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Abstract. Group classification is implemented for a pseudoparabolic partial differential equation with two parameters. Equivalence transformations groups are found and used for classification of the equation parameters. Kernels of principal symmetries groups are found for the equations. Principal symmetries groups are found for specifications of parameters expanding the kernel of transformations groups. The obtained submodels are summarized in a table at the end of the paper.

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Group classification of the equations of two-dimensional motions of a gas

Cited by 52 publications

References 1 publication

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

Group analysis of nonlinear fin equations

Group classification of a class of semilinear pseudoparabolic equations

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