Exact solutions of diffusion-convection equations

Abstract

In the presented paper known (up to the beginning of 2008) Lie-and non-Lie exact solutions of different (1 + 1)-dimensional diffusion-convection equations of form f (x)u t = (g(x)A(u)u x ) x + h(x)B(u)u x are collected.

Symmetry analysis of nonlinear heat and mass transfer equations under Soret effect

“…There are a lot of handbooks and manuscripts devoted to demonstration, construction and analysis of the exact solutions of various nonlinear partial differential equations (see, e.g., [17][18][19]). A collection of exact solutions (1+1)-dimensional diffusion-convection equations is presented in [20]. To give a physical interpretation of these solutions is not a purpose of that work.…”

Group analysis of(2+1)- and(3+1)-dimensional diffusion–convection e

“…Also equations in the entries 3b and 7b are linear equations. The lists of known exact solutions of these equations can be found, e.g., in [11,18]. Table 4 Subalgebras Δ i , similarity variables, similarity solutions and reduced equations for (3)…”

“…Equivalence group G ∼ 3 of class (2) consists of the 11-parameter group of point transformations: t = ε 6 t + ε 1 ,x = ε 7 x + ε 11 t + ε 2 ,ỹ = ε 8 y + ε 3 ,z = ε 9 z + ε 4 ,ũ = ε 10 u + ε 5 , 11 , where ε 1 , . .…”

Type II hidden symmetries for the homogeneous heat equation in some general classes of Riemannian spaces

“…In what follows all spaces are of dimension n 2. The case n = 1 although relatively trivial for our approach in general it is not so and has been studied for example in [18,19].…”