Dynamic materials with formation of clots: optimal mass transport in one spatial dimension without takeover

The concept of dynamic materials (DM) was introduced in the earlier work [1, 2, 9] and developed there for the case of non-colliding characteristics. The present paper extends this concept toward the case when the characteristics collide. The extension is formulated for a linear continuity equation in 1D with a no takeover condition applied to the moving masses. This implies the formation of clots with the preservation of both mass and momentum, which makes the approach resemble the method of “sticky particles” known in pressureless gas dynamics. The extension introduces non-linearity into the transportation problem that was originally missing, thus placing it closer to a non-linear conservation law.