TY - JOUR
T1 - Compactness Framework ofLpApproximate Solutions for Scalar Conservation Laws
AU - Yang, Tong
AU - Zhu, Changjiang
AU - Zhao, Huijiang
PY - 1998/4/1
Y1 - 1998/4/1
N2 - In this paper, we study the strong convergence of a sequence of uniformLp
loc(R×R+) bounded approximate solutions {uε(x,t)} to the following scalar conservation laws[formula]with initial data[formula]Without the convexity assumption and growth condition at infinity forf(x,t,u), we prove strong convergence of a subsequence of {uε(x,t)}. Under a more general growth condition than those in the previous work, we prove the existence of weak solution for the equation. The result obtained here generalizes those in earlier work. Some applications of the results are also given at the end of this paper. © 1998 Academic Press.
AB - In this paper, we study the strong convergence of a sequence of uniformLp
loc(R×R+) bounded approximate solutions {uε(x,t)} to the following scalar conservation laws[formula]with initial data[formula]Without the convexity assumption and growth condition at infinity forf(x,t,u), we prove strong convergence of a subsequence of {uε(x,t)}. Under a more general growth condition than those in the previous work, we prove the existence of weak solution for the equation. The result obtained here generalizes those in earlier work. Some applications of the results are also given at the end of this paper. © 1998 Academic Press.
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U2 - 10.1006/jmaa.1997.5845
DO - 10.1006/jmaa.1997.5845
M3 - 21_Publication in refereed journal
VL - 220
SP - 164
EP - 186
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -