New singular travelling waves for convection-diffusion-reaction equations

The present paper studies, strictly within the theory of distributions, the propagation of travelling waves with a distributional profile in one-dimensional models ruled by convection-diffusion-reaction equations. By applying a product of distributions (not defined by approximation processes), a rigorous concept of a solution which extends the classical solution concept is defined. As a consequence we establish necessary and sufficient conditions for the propagation of a distributional profile. The use of these conditions enable us to see the appearance of shock waves, delta waves and also delta shock travelling waves. The main ideas and formulas needed for multiplying distributions are included for the reader's convenience.