ON APPROXIMATE SELF-SIMILAR SOLUTIONS OF A CLASS OF QUASILINEAR HEAT EQUATIONS WITH A SOURCE
Vladimir Alexandrovich Galaktionov, Sergei P. Kurdyumov, A. A. Samarskiĭ · Mathematics of the USSR-Sbornik · 1985
Quasilinear parabolic equations of the form are considered; here and are sufficiently smooth given functions (respectively, the coefficient of thermal conductivity and the power of heat sources depending on the temperature ). A family of coefficients and corresponding functions is distinguished for which the properties of the solution of the boundary value problem for the equation in question is described by invariant solutions of a first-order equation of Hamilton-Jacobi type The function is an approximate self-similar solution of the original equation. Tables: 1. Figures: 1. Bibliography: 70 titles.