Abstract <p> This paper examines the equation of autowave diffusion with a discontinuous source. Conditions are formulated under which an autowave can pass through the interface between media. Here the direction of the autowave’s motion is maintained, while its velocity changes in magnitude. An approximate law of motion of the autowave front is obtained, and an existence theorem is proved. The primary research method is the asymptotic method of differential inequalities. The results of this paper can be used to describe the propagation of autowaves in layered media and to solve inverse problems determining the characteristics of such media. The study of the process of autowave propagation in layered media can be used to develop diverse biophysical models, such as the spatially heterogeneous distribution of populations in habitats, the territorial development of megacities, and patterns of cancer cell proliferation. </p>