Wavefronts and unbounded waves for power-law equations

Abstract

With the porous media equation as prototype, equations of the class (1.1) with power-law coefficients have attracted much interest to date. In this chapter, we shall classify all the global monotonic travelling-wave solutions decreasing to 0 and all the unbounded monotonic semi-wavefront solutions decreasing to 0 for equations of this type. We begin with the power-law convection-diffusion equation, proceed to the power-law reaction-diffusion equation with linear convection, and, end with the full equation.