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.
Citation:
V. A. Galaktionov, V. A. Dorodnitsyn, G. G. Yelenin, S. P. Kurdyumov, A. A. Samarskii, “A quasilinear equation of heat conduction with a source: peaking, localization, symmetry, exact solutions, asymptotic behavior, structures”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 28, VINITI, Moscow, 1986, 95–205; J. Soviet Math., 41:5 (1988), 1222–1292
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