Abstract
The conditional invariance of the nonlinear heat equation is studied. Conditionalinvariance operators are applied for reducing the original equation to ordinary differential equations, and also for finding its exact solutions.
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L. V. Ovsyannikov, “Group properties of the nonlinear heat equation,” Dokl. Akad. Nauk SSSR,125, 492–495 (1959).
V. A. Dorondnytsyn, I. V. Knyazeva, and S. R. Svishchevskii, “Group properties of the heat equation with a source in two-dimensional and three-dimensional cases,” Differents. Uravn.,19, No. 7, 1215–1224 (1983).
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V. I. Fushchich, V. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Moscow (1989).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 10, pp. 1370–1376, October, 1990.
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Serov, N.I. Conditional invariance and exact solutions of the nonlinear equation. Ukr Math J 42, 1216–1222 (1990). https://doi.org/10.1007/BF01057392
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DOI: https://doi.org/10.1007/BF01057392