The δ′ wave solution to a totally degenerate system of conservation laws

Products of distributions and the problem of galactic rotation

“…Journal of Mathematical Physics ARTICLE pubs.aip.org/aip/jmp and (25) follows immediately. Also from (21) and (22) we get (23) and (24) and it is now easy to see that conditions (1 ′ ), (2 ′ ), (3 ′ ), (4 ′ ) and (5 ′ ) are all satisfied for all t. Clearly, this α-solution is unique in W and does not depend on α. The value of ρ(t) follows from (22).…”

“…Certainly this is one of the reasons for which several authors begun to adopt this method (see Refs. [18][19][20][21][22][23][24][25][26][27][28][29][30]. Another reason regards to important simplifications: the Rankine-Hugoniot shock conditions and their multiple generalizations are not necessary and, as much as we know, the final result is the same (see Refs.…”

“…Interestingly, in a recent paper, 23 Pang et al compared the exact α-solutions of a totally degenerate system of conservation laws, with the numerical solutions obtained by using the Nessyahu-Tadmor scheme: the α-solutions coincide with the corresponding numerical solutions. For more problems where the concept of α-solution was also applied the reader may see Refs.…”