Existence of global bounded weak entropy solutions to extended Keyfitz–Kranzer system modelling polymer flooding
Abstract: In this paper, the Cauchy problem for extended Keyfitz–Kranzer system of conservation laws modelling polymer flooding is studied, and a short proof of global existence of weak entropy solutions is obtained by using a new technique from the compensated compactness theorem coupled with the total variation estimate on one family of Riemann invariant. This work extends in some sense the previous works, [Barkve, SIAM J. on Appl. Math., 49(1989), 784–798] and [Johansen and Winther, SIAM J. Math. Anal., 19 (1988), 541–566], which provided the global existence of weak solutions for Riemann problem; and [Lu, J. Funct. Anal., 261(2011), 2797–2815], which gave the global weak solution of the Cauchy problem for nonstrictly hyperbolic system of Keyfitz–Kranzer or Aw–Rascle type.