Embedded delta shocks

Abstract

In 1977 Korchinski presented a new type of shock discontinuity in conservation laws. These singular solutions were coined -shocks since there is a time dependent Dirac delta involved. A naive description is that suchshock is of the overcompressive type: a single shock wave belonging to both families, the four characteristic lines of which impinge into the shock itself. In this work, we open the fan of solutions by studying two-family waves without intermediate constant states but possessing central rarefactions or comprising -shocks.where is zero or one, and and are linear in , see also [3]. We identify the Riemann solution by = ( , ) ⊤ .Consider the case = 0 and notice that for a Riemann problem including a -shock, the shock speed is extracted from (5a), and from

The Perturbed Riemann Problem for a Macroscopic Production Model with Chaplygin Gas

“…In the current work, the strength β(t) in (2.13) is obtained by virtue of the fact that all of the mass gathering together on the line of δ J only comes from the particles on the right-hand side of it. It is of great interest to notice that the solution consisting of delta shock wave surrounded by two rarefaction waves on both sides of delta shock line has been constructed in [39] recently, which is similar to the composite wave Rδ J in this paper. In conclusion, the Riemann solutions of (1.2) and (1.3) are constructed fully for all the possible cases, namely S + J for u − < u + , R + J for (ρ − −1)u − ρ − < u + < u − , as well as Rδ J for 0…”

Improving Woody Biomass Pellets in Residential Application

“…Saw dust-Sawdust is the waste which is found by chip formation of wood which is further used in the particle wood, manufacturing wooden tables etc (8).…”