<p style='text-indent:20px;'>We study a porous medium equation with dissipative and hyperdiffusive effects no sign restrictions on the diffusion coefficient.</p>

When a broadband pulse penetrates into a dissipative and dispersive medium, phase dispersion and frequency-dependent attenuation alter the pulse in a way that results in the appearance of a precursor field with an algebraic decay. We derive here the existence of precursors in nondispersive, non-dissipative, but randomly heterogeneous and multiscale media. The shape of the precursor and its frac...