Symmetries of Fundamental Solutions and Their Application in Continuum Mechanicsстатья
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Scopus
Статья опубликована в журнале из перечня ВАК
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 10 августа 2018 г.
Аннотация:An application of the symmetries of fundamental solutions in continuum mechanics is presented. It is shown that the Riemann function of a second-order linear hyperbolic equation in two independent variables is invariant with respect to the symmetries of fundamental solutions,
and a method is proposed for constructing such a function. A fourth-order linear elliptic
partial differential equation is considered that describes the displacements of a transversely
isotropic linear elastic medium. The symmetries of this equation and the symmetries of the
fundamental solutions are found. The symmetries of the fundamental solutions are used to
construct an invariant fundamental solution in terms of elementary functions.