TY - JOUR
T1 - Existence in the large for riemann problems for systems of conservation laws
AU - Sever, Michael
PY - 1985/11
Y1 - 1985/11
N2 - An existence theorem in the large is obtained for the Riemann problem for nonlinear systems of conservation laws. Our principal assumptions are strict hyperbolicity, genuine nonlinearity in the strong sense, and the existence of a convex entropy function. The entropy inequality is used to obtain an a priori estimate of the strengths of the shocks and refraction waves forming a solution; existence of such a solution then follows by an application of finite-dimensional degree theory. The case of a single degenerate field is also included, with an additional assumption on the existence of Riemann invariants.
AB - An existence theorem in the large is obtained for the Riemann problem for nonlinear systems of conservation laws. Our principal assumptions are strict hyperbolicity, genuine nonlinearity in the strong sense, and the existence of a convex entropy function. The entropy inequality is used to obtain an a priori estimate of the strengths of the shocks and refraction waves forming a solution; existence of such a solution then follows by an application of finite-dimensional degree theory. The case of a single degenerate field is also included, with an additional assumption on the existence of Riemann invariants.
UR - http://www.scopus.com/inward/record.url?scp=84967763061&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1985-0805969-5
DO - 10.1090/S0002-9947-1985-0805969-5
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AN - SCOPUS:84967763061
SN - 0002-9947
VL - 292
SP - 375
EP - 381
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 1
ER -