  The blast caused by an intense explosion has been extensively studied in
conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution
is a prototypical example of self-similarity driven by conservation laws. In
dissipative media however, energy conservation is violated, yet a distinctive
self-similar solution appears. It hinges on the decoupling of random and
coherent motion permitted by a broad class of dissipative mechanisms. This
enforces a peculiar layered structure in the shock, for which we derive the
full hydrodynamic solution, validated by a microscopic approach based on
Molecular Dynamics simulations. We predict and evidence a succession of
temporal regimes, as well as a long-time corrugation instability, also
self-similar, which disrupts the blast boundary. These generic results may
apply from astrophysical systems to granular gases, and invite further
cross-fertilization between microscopic and hydrodynamic approaches of
shockwaves.
