TY - JOUR
T1 - Exchange of conserved quantities in nonhyperbolic systems-an example
AU - Sever, Michael
PY - 2001
Y1 - 2001
N2 - The velocity function associated with a smooth solution of "zero pressure gas dynamics" satisfies Burgers equation. Indeed an elementary generalization holds for scalar conservation laws. Weak solutions, however, are compatible in this respect only under special conditions on the initial density function. Our result depends on the uniform convexity of the flux function associated with the scalar equation, and on the entropy condition applied to both systems.
AB - The velocity function associated with a smooth solution of "zero pressure gas dynamics" satisfies Burgers equation. Indeed an elementary generalization holds for scalar conservation laws. Weak solutions, however, are compatible in this respect only under special conditions on the initial density function. Our result depends on the uniform convexity of the flux function associated with the scalar equation, and on the entropy condition applied to both systems.
UR - http://www.scopus.com/inward/record.url?scp=33646851268&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-01-06316-x
DO - 10.1090/s0002-9939-01-06316-x
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AN - SCOPUS:33646851268
SN - 0002-9939
VL - 129
SP - 3671
EP - 3681
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 12
ER -