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Gruppovoi analiz differentsial'nykh uravnenii
A. Aksenov (1995)
Symmetries of linear partial differemtial equations and fundamental solutionsDoklady Mathematics, 51
D. Georgievskiĭ (2015)
The Galerkin tensor operator, reduction to tetraharmonic equations, and their fundamental solutionsDoklady Physics, 60
G. Bluman (1990)
Simplifying the form of Lie groups admitted by a given differential equationJournal of Mathematical Analysis and Applications, 145
(1995)
Symmetries and fundamental solutions of the multidimensional generalized axisymmetric Laplace equation
(1979)
Obobshchennye funktsii v matematicheskoi fizike (Generalized Functions in Mathematical Physics)
V.S. Vladimirov (1979)
Obobshchennye funktsii v matematicheskoi fizike
D. Georgievskiĭ (2015)
An extended Galerkin representation for a transversely isotropic linearly elastic mediumJournal of Applied Mathematics and Mechanics, 79
We consider a linear fourth-order elliptic partial differential equation describing the displacements of a transversely isotropic linearly elastic medium. We find the symmetries of this equation and of the inhomogeneous equation with the delta function on the right-hand side. Based on the symmetries of the inhomogeneous equation, we construct an invariant fundamental solution in elementary functions.
Differential Equations – Springer Journals
Published: Jun 14, 2017
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