Separation of variables of a generalized porous medium equation with nonlinear source

[摘要] This paper considers a general form of the porous medium equation with nonlinear source term: u(t) = (D(u)u(x)(n))(x) + F(u), n not equal 1. The functional separation of variables of this equation is studied by using the generalized conditional symmetry approach. We obtain a complete list of canonical forms for such equations which admit the functional separable solutions. As a consequence, some exact solutions to the resulting equations are constructed, and their behavior are also investigated. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-11-01

[关键词] separation of variable;symmetry group;generalized conditional symmetry;nonlinear diffusion equation;exact solution