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A quasilinear heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures

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Abstract

A survey is given of results of investigating unbounded solutions (regimes with peaking) of quasilinear parabolic equations of nonlinear heat conduction with a source. Principal attention is devoted to the investigation of the property of localization of regimes with peaking. A group classification of nonlinear equations of this type is carried out, properties of a broad set of invariant (self-similar) solutions are investigated, and special methods of investigating the space-time structure of unbounded solutions are developed.

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Authors
  1. V. A. Galaktionov
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  2. V. A. Dorodnitsyn
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  3. G. G. Elenin
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  4. S. P. Kurdyumov
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  5. A. A. Samarskii
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 28, pp. 95–206, 1986.

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Galaktionov, V.A., Dorodnitsyn, V.A., Elenin, G.G. et al. A quasilinear heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures. J Math Sci 41, 1222–1292 (1988). https://doi.org/10.1007/BF01098785

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