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Group properties of the heat-conduction equation with a source in the two- and three-dimensional cases. (English. Russian original) Zbl 0541.35036
Differ. Equations 19, 901-908 (1983); translation from Differ. Uravn. 19, No. 7, 1215-1223 (1983).
The group classification for the heat equation with a source (or sink) \(\partial T/\partial t=\sum^{N}_{i=1}(\partial /\partial x_ i)(K_ i(T)\partial T/\partial x_ i)+Q(T), K_ i(T)\geq 0; N=2,3\) is given. The group of equivalence transformations can be represented in the form \(x'\!_ i=a_ ibx_ i+e_ i;\quad t'=b^ 2t+f;\quad T'=cT+d; K'\!_ i(T')=a^ 2_ iK_ i(T^ 1/c-d/c); Q'(T')=(c/b^ 2)Q(T'/c-d/c), a_ ibc\neq 0\), \(i=1,...,N\).
Reviewer: L.A.Sakhnović

MSC:
35K10 Second-order parabolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
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