Traveling Wave Solution for Some Nonlinear Diffusion Equations

Source abstract

Traveling wave solutions are discussed for nonlinear diffusion equations where the nonlinearity occurs in the diffusion flux as well as in a source term. For a variety of nonlinear diffusion fluxes it is shown that wave solutions exist if and only if the wave speed is greater than some critical value. This critical value is determined explicitly in some special cases, and inequalities are derived for the general case.