Kaptsov, O. V. Invariant tensors and partial differential equations. (Russian, English) Zbl 1115.35014 Sib. Mat. Zh. 47, No. 2, 316-328 (2006); translation in Sib. Math. J. 47, No. 2, 258-268 (2006). Summary: We consider tensors with coefficients in a commutative differential algebra \(A\). Using the Lie derivative, we introduce the notion of a tensor invariant under a derivation on an ideal of \(A\). Each system of partial differential equations generates an ideal in some differential algebra. This makes it possible to study invariant tensors on such an ideal. As examples we consider the equations of gas dynamics and magnetohydrodynamics. MSC: 35A30 Geometric theory, characteristics, transformations in context of PDEs 35L65 Hyperbolic conservation laws 35Q35 PDEs in connection with fluid mechanics 76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics Keywords:integral invariant; Lie derivative; invariant tensor PDFBibTeX XMLCite \textit{O. V. Kaptsov}, Sib. Mat. Zh. 47, No. 2, 316--328 (2006; Zbl 1115.35014); translation in Sib. Math. J. 47, No. 2, 258--268 (2006) Full Text: EuDML EMIS