Abstract

This paper studies a class of second order partial differential equations *utt = f(ux)uxx + g(ut)* arising in poroelasticity theory with arbitrary functions *f(ux)* and *g(ut)*, using the group classification. It is shown that the principal Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of a preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

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yusupov.pdf178.38 KB

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79-84