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Abstract |
Explicit Solutions of Nonlinear Heat
Equations
O.Kaptsov, I.V.Verevkin (Institute of
Computing Modelling RAS, Academgorodok, Krasnoyarsk, Russia)
e-mail:
kaptsov@ksc.krasn.ru
It
was recently proposed a new method for finding differential constraints which
uses linear determining equations. These equations are more general than the
classical determining equations for Lie generators [1] and depend on some
parameters. In this report we start with determination of the solutions of
linear determining equations of the second and third orders for the nonlinear
diffusion equation. Then we use the
obtained functions to find solutions of nonlinear heat equations. At last we
derive exact solutions of some two-dimension equation. Bibliography O.V.Kaptsov (1998) Linear determining
equations for differential constraints. Sbornik: Mathematics 189: 12 1839-1854
Section
: 12