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